Edit Profile (opens in new tab) Grigor’yan, Alexander Asaturovich Compute Distance To: Compute Author ID: grigoryan.alexander Published as: Grigor’yan, Alexander; Grigor’yan, A. A.; Grigor’yan, A.; Grigoryan, A.; Grigoryan, A. A.; Grigor’yan, Alexander A. more...less Homepage: http://www.math.uni-bielefeld.de/~grigor/ External Links: Math-Net.Ru Documents Indexed: 140 Publications since 1979, including 2 Books 5 Contributions as Editor Co-Authors: 85 Co-Authors with 101 Joint Publications 3,318 Co-Co-Authors all top 5 Co-Authors 44 single-authored 16 Yau, Shing-Tung 15 Hu, Jiaxin 11 Muranov, Yuriĭ Vladimirovich 9 Coulhon, Thierry 8 Lau, Kasing 8 Saloff-Coste, Laurent 6 Lin, Yong 5 Bendikov, Alexander D. 4 Hu, Eryan 4 Jiménez Benitez, Rolando 4 Kelbert, Mark Ya. 4 Nadirashvili, Nikolai S. 4 Sun, Yuhua 3 Barlow, Martin T. 3 Chung, Fan 3 Ishiwata, Satoshi 3 Kumagai, Takashi 3 Pittet, Christophe 3 Telcs, András 3 Verbitsky, Igor E. 3 Yang, Yunyan 2 Cao, Jun 2 Fokas, Athanassios S. 2 Hansen, Wolfhard 2 Huang, Xueping 2 Kibble, Tom W. B. 2 Liu, Liguang 2 Masamune, Jun 2 Molchanov, Stanislav Alekseevich 2 Yang, Meng 2 Zegarlinski, Boguslaw 1 Auscher, Pascal 1 Avkhadiev, Farit Gabidinovich 1 Barabasheva, Yu. M. 1 Botvinnik, V. A. 1 Chirka, Evgeni M. 1 Devyatkova, G. N. 1 Drinfeld, Vladimir Gershonovich 1 Dubinin, Vladimir N. 1 Faraji, Shokoufe 1 Gilkey, Peter B. 1 Gol’dstein, Vladimir Mikailovitch 1 Goryainov, Viktor V. 1 Hsu, Elton P. 1 Ilyashenko, Yulij Sergeevich 1 Jakobson, Dmitry 1 Kajino, Naotaka 1 Kenig, Carlos Eduardo 1 Kesel’man, V. M. 1 Kirsten, Klaus 1 Klyachin, Vladimir Aleksandrovich 1 Kondrat’ev, Vladimir Aleksandrovich 1 Kondrat’yev, Yuriĭ Grygorovych 1 Kuksin, Sergeĭ B. 1 Latfullin, T. G. 1 Levin, Daniel 1 Loboda, Alexander Vasil’evich 1 Martio, Olli 1 Netrusov, Yuri 1 Noguchi, Masakazu 1 Ouyang, Shunxiang 1 Pelikh, V. I. 1 Piatnitski, Andrey L. 1 Pinchuk, Sergey 1 Reshetnyak, Yuriĭ Grigor’evich 1 Röckner, Michael 1 Romanov, Aleksandr Sergeevich 1 Samorodnitsky, Gennady Pinkhosovich 1 Sarnak, Peter Clive 1 Sergeev, Armen Glebovich 1 Sire, Yannick 1 Tkachev, Vladimir G. 1 Tsfasman, Michael A. 1 Tutubalin, Valeriĭ Nikolaevich 1 Uger, E. G. 1 van den Berg, Michiel 1 Vershinin, Vladimir V. 1 Vlǎduţ, Sergei Georgievich 1 Vodop’yanov, Sergeĭ Konstantinovich 1 Vuorinen, Matti Keijo Kustaa 1 Woess, Wolfgang 1 Zhizhina, Elena Anatol’evna 1 Zhuravlëv, I. V. 1 Zorich, Vladimir Antonovich 1 Zucca, Fabio all top 5 Serials 6 Journal of Functional Analysis 4 Mathematical Notes 4 Russian Mathematical Surveys 4 Transactions of the American Mathematical Society 4 Communications in Analysis and Geometry 3 Communications on Pure and Applied Mathematics 3 Annales de l’Institut Fourier 3 The Annals of Probability 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Mathematics of the USSR, Sbornik 2 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 2 Journal d’Analyse Mathématique 2 Advances in Mathematics 2 Duke Mathematical Journal 2 Inventiones Mathematicae 2 Journal of Differential Geometry 2 Journal of the Mathematical Society of Japan 2 Journal für die Reine und Angewandte Mathematik 2 Matematicheskiĭ Sbornik. Novaya Seriya 2 Mathematische Annalen 2 Soviet Mathematics. Doklady 2 Soviet Mathematics 2 Revista Matemática Iberoamericana 2 Forum Mathematicum 2 Calculus of Variations and Partial Differential Equations 2 Homology, Homotopy and Applications 2 Moscow Mathematical Journal 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Moscow University Mathematics Bulletin 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 American Journal of Mathematics 1 Bulletin of the London Mathematical Society 1 Canadian Journal of Mathematics 1 Czechoslovak Mathematical Journal 1 Journal of Differential Equations 1 Journal of the London Mathematical Society. Second Series 1 Journal of Soviet Mathematics 1 Mathematics of the USSR. Izvestiya 1 Mathematische Zeitschrift 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the London Mathematical Society. Third Series 1 Tohoku Mathematical Journal. Second Series 1 Voprosy Istorii Estestvoznaniya i Tekhniki 1 Topology and its Applications 1 Probability Theory and Related Fields 1 Geometric and Functional Analysis. GAFA 1 Communications in Partial Differential Equations 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 1 Bulletin of the American Mathematical Society. New Series 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Matematicheskiĭ Sbornik 1 Potential Analysis 1 Journal of Mathematical Sciences (New York) 1 Mathematical Research Letters 1 Izvestiya: Mathematics 1 The Journal of Fourier Analysis and Applications 1 Istoriko-Matematicheskie Issledovaniya. Vtoraya Seriya 1 The Asian Journal of Mathematics 1 Pure and Applied Mathematics Quarterly 1 Rendiconti del Seminario Matematico. Universitá e Politecnico di Torino 1 Contemporary Mathematics 1 University Lecture Series 1 AMS/IP Studies in Advanced Mathematics 1 Surveys in Differential Geometry 1 Journal of Homotopy and Related Structures 1 Science China. Mathematics 1 Global and Stochastic Analysis 1 Journal of Fractal Geometry 1 Advances in Analysis and Geometry all top 5 Fields 78 Global analysis, analysis on manifolds (58-XX) 60 Partial differential equations (35-XX) 43 Probability theory and stochastic processes (60-XX) 24 Potential theory (31-XX) 19 Measure and integration (28-XX) 17 Operator theory (47-XX) 15 Combinatorics (05-XX) 14 Differential geometry (53-XX) 10 Algebraic topology (55-XX) 9 Functional analysis (46-XX) 5 General and overarching topics; collections (00-XX) 5 History and biography (01-XX) 5 Category theory; homological algebra (18-XX) 5 Manifolds and cell complexes (57-XX) 3 Real functions (26-XX) 3 Functions of a complex variable (30-XX) 3 Ordinary differential equations (34-XX) 2 Group theory and generalizations (20-XX) 2 Difference and functional equations (39-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 2 General topology (54-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Topological groups, Lie groups (22-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Convex and discrete geometry (52-XX) 1 Quantum theory (81-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 121 Publications have been cited 2,285 times in 1,259 Documents Cited by ▼ Year ▼ Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds. Zbl 0927.58019Grigor’yan, Alexander 298 1999 Heat kernel and analysis on manifolds. Zbl 1206.58008Grigor’yan, Alexander 142 2009 Heat kernel upper bounds on a complete non-compact manifold. Zbl 0810.58040Grigor’yan, Alexander 65 1994 Heat kernels on weighted manifolds and applications. Zbl 1106.58016Grigor’yan, Alexander 62 2006 Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds. Zbl 0865.58042Grigor’yan, Alexander 59 1997 Heat kernels on metric measure spaces and an application to semilinear elliptic equations. Zbl 1018.60075Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 55 2003 Heat kernel upper bounds for jump processes and the first exit time. Zbl 1158.60039Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi 54 2009 Two-sided estimates of heat kernels on metric measure spaces. Zbl 1252.35148Grigor’yan, Alexander; Telcs, Andras 49 2012 Stability results for Harnack inequalities. Zbl 1115.58024Grigor’yan, Alexander; Saloff-Coste, Laurent 47 2005 Random walks on graphs with regular volume growth. Zbl 0918.60053Coulhon, T.; Grigoryan, A. 46 1998 Sub-Gaussian estimates of heat kernels on infinite graphs. Zbl 1010.35016Grigor’yan, Alexander; Telcs, Andras 41 2001 Harnack inequalities and sub-Gaussian estimates for random walks. Zbl 1011.60021Grigor’yan, A.; Telcs, A. 40 2002 Estimates of heat kernels on Riemannian manifolds. Zbl 0985.58007Grigor’yan, Alexander 40 1999 The heat equation on noncompact Riemannian manifolds. Zbl 0776.58035Grigor’yan, A. A. 38 1992 On the equivalence of parabolic Harnack inequalities and heat kernel estimates. Zbl 1281.58016Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi 38 2012 Heat equation on noncompact Riemannian manifolds. Zbl 0743.58031Grigor’yan, A. A. 36 1991 On stochastically complete manifolds. Zbl 0632.58041Grigor’yan, A. A. 35 1987 Heat kernels and function theory on metric measure spaces. Zbl 1048.58021Grigor’yan, Alexander 35 2003 Yamabe type equations on graphs. Zbl 1351.35038Grigor’yan, Alexander; Lin, Yong; Yang, Yunyan 35 2016 On-diagonal lower bounds for heat kernels and Markov chains. Zbl 0920.58064Coulhon, Thierry; Grigor’yan, Alexander 34 1997 On stochastic completeness of jump processes. Zbl 1408.60076Grigor’yan, Alexander; Huang, Xueping; Masamune, Jun 32 2012 Manifolds and graphs with slow heat kernel decay. Zbl 1003.58025Barlow, Martin; Coulhon, Thierry; Grigor’yan, Alexander 32 2001 Dirichlet heat kernel in the exterior of a compact set. Zbl 1037.58018Grigor’yan, Alexander; Saloff-Coste, Laurent 31 2002 Kazdan-Warner equation on graph. Zbl 1366.58006Grigor’yan, Alexander; Lin, Yong; Yang, Yunyan 31 2016 Upper bounds of derivatives of the heat kernel on an arbitrary complete manifold. Zbl 0842.58070Grigor’yan, Alexander 31 1995 Upper bounds of heat kernels on doubling spaces. Zbl 06332192Grigor’yan, Alexander; Hu, Jiaxin 27 2014 Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces. Zbl 1154.47034Grigor’yan, Alexander; Hu, Jiaxin 26 2008 Heat kernel on manifolds with ends. Zbl 1239.58016Grigor’yan, Alexander; Saloff-Coste, Laurent 25 2009 Isotropic Markov semigroups on ultra-metric spaces. Zbl 1322.60151Bendikov, A. D.; Grigor’yan, A. A.; Pittet, Ch; Woess, W. 22 2014 Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs. Zbl 1001.58022Chung, Fan; Grigor’yan, Alexander; Yau, Shing-Tung 22 2000 On the existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds. Zbl 0612.31007Grigor’yan, A. A. 21 1987 On nonnegative solutions of the inequality \(\Delta u+u^{\sigma }\leq 0\) on Riemannian manifolds. Zbl 1296.58011Grigor’yan, Alexander; Sun, Yuhua 21 2014 A Liouville property for Schrödinger operators. Zbl 0938.31007Grigor’yan, Alexander; Hansen, Wolfhard 21 1998 A geometric approach to on-diagonal heat kernel lower bounds on groups. Zbl 1137.58307Coulhon, Thierry; Grigor’yan, Alexander; Pittet, Christophe 21 2001 The heat kernel of hyperbolic space. Zbl 0921.58063Grigor’yan, Alexander; Noguchi, Masakazu 21 1998 Escape rate of Brownian motion on Riemannian manifolds. Zbl 1020.58024Grigor’yan, Alexander 21 1999 Parabolicity and stochastic completeness of manifolds in terms of the Green formula. Zbl 1356.58007Grigor’yan, Alexander; Masamune, Jun 20 2013 Eigenvalues of elliptic operators and geometric applications. Zbl 1061.58027Grigor’yan, Alexander; Netrusov, Yuri; Yau, Shing-Tung 20 2004 Heat kernels and Green functions on metric measure spaces. Zbl 1293.35128Grigor’yan, Alexander; Hu, Jiaxin 20 2014 Upper bounds for eigenvalues of the discrete and continuous Laplace operators. Zbl 0844.53029Chung, F. R. K.; Grigor’yan, A.; Yau, Shing-Tung 20 1996 Hitting probabilities for Brownian motion on Riemannian manifolds. Zbl 1042.58022Grigor’yan, Alexander; Saloff-Coste, Laurent 20 2002 The discrete integral maximum principle and its applications. Zbl 1096.60023Coulhon, Thierry; Grigor’yan, Alexander; Zucca, Fabio 19 2005 Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces. Zbl 1331.35152Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 19 2015 Estimates of heat kernels for non-local regular Dirichlet forms. Zbl 1304.47058Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 18 2014 Integral maximum principle and its applications. Zbl 0812.58082Grigor’yan, Alexander 18 1994 Existence of positive solutions to some nonlinear equations on locally finite graphs. Zbl 1384.34035Grigor’yan, Alexander; Lin, Yong; Yang, YunYan 17 2017 Comparison inequalities for heat semigroups and heat kernels on metric measure spaces. Zbl 1207.58021Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 16 2010 On the dichotomy in the heat kernel two sided estimates. Zbl 1162.47037Grigor’yan, Alexander; Kumagai, Takashi 15 2008 Stochastically complete manifolds and summable harmonic functions. Zbl 0677.60086Grigor’yan, A. A. 13 1989 Homotopy theory for digraphs. Zbl 1312.05063Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung 13 2014 Existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds. Zbl 0596.31004Grigor’yan, A. A. 13 1985 Isoperimetric inequalities and capacities on Riemannian manifolds. Zbl 0947.58034Grigor’yan, Alexander 12 1999 On isoperimetric profiles of product spaces. Zbl 1085.53027Coulhon, Thierry; Grigor’yan, Alexander; Levin, Daniel 12 2003 Range of fluctuation of Brownian motion on a complete Riemannian manifold. Zbl 0934.58023Grigor’yan, Alexander; Kelbert, Mark 11 1998 Heat kernels on metric spaces with doubling measure. Zbl 1197.35129Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 11 2009 Isoperimetric properties of higher eigenvalues of elliptic operators. Zbl 1042.58017Grigor’yan, Alexander; Yau, Shing-Tung 11 2003 Two-sided estimates of heat kernels of jump type Dirichlet forms. Zbl 1468.35081Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 11 2018 Heat kernel on connected sums of Riemannian manifolds. Zbl 0957.58023Grigor’yan, Alexander; Saloff-Coste, Laurent 11 1999 Heat kernels on metric measure spaces with regular volume growth. Zbl 1217.58018Grigor’yan, Alexander 10 2010 On a class of Markov semigroups on discrete ultra-metric spaces. Zbl 1260.60142Bendikov, Alexander; Grigor’yan, Alexander; Pittet, Christophe 10 2012 On the existence of positive solutions of semilinear elliptic inequalities on Riemannian manifolds. Zbl 1185.35344Grigor’yan, Alexander; Kondratiev, Vladimir A. 10 2010 On the existence of a Green’s function on a manifold. Zbl 0542.35025Grigor’yan, A. A. 10 1983 Surgery of the Faber-Krahn inequality and applications to heat kernel bounds. Zbl 1334.58019Grigor’yan, Alexander; Saloff-Coste, Laurent 10 2016 Heat kernel on a manifold with a local Harnack inequality. Zbl 0845.58056Grigor’yan, Alexander 9 1994 Heat kernels on metric measure spaces. Zbl 1323.58018Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 9 2014 Negative eigenvalues of two-dimensional Schrödinger operators. Zbl 1319.35128Grigor’yan, Alexander; Nadirashvili, Nikolai 9 2015 Introduction to analysis on graphs. Zbl 1416.05002Grigor’yan, Alexander 9 2018 Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces. Zbl 1372.35123Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 9 2017 Volume growth and escape rate of Brownian motion on a Cartan-Hadamard manifold. Zbl 1167.58019Grigor’yan, Alexander; Hsu, Elton 8 2009 Lower estimates for a perturbed Green function. Zbl 1158.35022Grigor’yan, Alexander; Hansen, Wolfhard 8 2008 Graphs associated with simplicial complexes. Zbl 1297.05269Grigor’yan, A.; Muranov, Yu. V.; Yau, Shing-Tung 8 2014 Heat kernel and Lipschitz-Besov spaces. Zbl 1327.35130Grigor’yan, Alexander; Liu, Liguang 8 2015 Decomposition of a metric space by capacitors. Zbl 0976.31006Grigor’yan, A.; Yau, S.-T. 8 1999 On Hardy-Littlewood inequality for Brownian motion on Riemannian manifolds. Zbl 1026.58028Grigor’yan, Alexander; Kelbert, Mark 7 2000 Cohomology of digraphs and (undirected) graphs. Zbl 1329.05132Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung 7 2015 Liouville theorems and external boundary value problems. Zbl 0639.58029Grigor’yan, A. A.; Nadirashvili, N. S. 6 1987 Stochastically complete manifolds and summable harmonic functions. Zbl 0661.60090Grigoryan, A. A. 6 1988 Obtaining upper bounds of heat kernels from lower bounds. Zbl 1148.58013Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 6 2008 Dimension of spaces of harmonic functions. Zbl 0721.31003Grigor’yan, A. A. 6 1990 Eigenvalues and diameters for manifolds and graphs. Zbl 0890.58093Chung, F. R. K.; Grigor’yan, A.; Yau, S.-T. 6 1997 On the path homology theory of digraphs and Eilenberg-Steenrod axioms. Zbl 1391.05125Grigor’yan, Alexander; Jimenez, Rolando; Muranov, Yuri; Yau, Shing-Tung 6 2018 Heat kernel of a noncompact Riemannian manifold. Zbl 0829.58041Grigor’yan, Alexander 6 1995 On Liouville theorems for harmonic functions with finite Dirichlet integral. Zbl 0646.31009Grigor’yan, A. A. 5 1987 Bounded solutions of the Schrödinger equation on noncompact Riemannian manifolds. Zbl 0744.58070Grigor’yan, A. A. 5 1989 Gaussian upper bounds for the heat kernel and for its derivatives on a Riemannian manifold. Zbl 0885.58088Grigor’yan, A. 5 1994 Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data. Zbl 1251.58009van den Berg, M.; Gilkey, Peter B.; Grigor’yan, A.; Kirsten, K. 5 2012 Heat kernel estimates on connected sums of parabolic manifolds. Zbl 1388.35078Grigor’yan, Alexander; Ishiwata, Satoshi; Saloff-Coste, Laurent 5 2018 Homologies of digraphs and Künneth formulas. Zbl 1381.05062Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung 5 2017 Isoperimetric inequalities for Riemannian products. Zbl 0599.53035Grigor’yan, A. A. 4 1985 Pointwise estimates for transition probabilities of random walks on infinite graphs. Zbl 1048.60081Coulhon, Thierry; Grigor’yan, Alexander 4 2003 On a cohomology of digraphs and Hochschild cohomology. Zbl 1353.05056Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung 4 2016 Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula. Zbl 1387.60121Grigor’yan, Alexander; Kajino, Naotaka 4 2017 Heat kernels, volume growth and anti-isoperimetric inequalities. Zbl 0873.58062Coulhon, Thierry; Grigor’yan, Alexander 3 1996 A lower bound for the number of negative eigenvalues of Schrödinger operators. Zbl 1356.53044Grigor’yan, Alexander; Nadirashvili, Nikolai; Sire, Yannick 3 2016 Stochastic completeness of symmetry Markov processes and volume growth. Zbl 1326.58020Grigor’yan, Alexander 3 2013 Heat kernels and analysis on manifolds, graphs, and metric spaces. Lecture notes from a quarter program on heat kernels, random walks, and analysis on manifolds and graphs, April 16–July 13, 2002, Paris, France. Zbl 1029.00030 3 2003 On a class of random perturbations of the hierarchical Laplacian. Zbl 1448.47050Bendikov, Alexander D.; Grigor’yan, Alexander A.; Molchanov, Stanislav A.; Samorodnitsky, Gennady P. 3 2015 Path homology theory of multigraphs and quivers. Zbl 1404.55010Grigor’yan, Alexander; Muranov, Yuri; Vershinin, Vladimir; Yau, Shing-Tung 3 2018 Pointwise estimates of solutions to semilinear elliptic equations and inequalities. Zbl 1421.35073Grigor’yan, Alexander; Verbitsky, Igor 3 2019 On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds. Zbl 1430.58014Grigor’yan, Alexander; Sun, Yuhua 3 2019 The pointwise existence and properties of heat kernel. Zbl 1476.35114Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 1 2021 Pointwise estimates of solutions to nonlinear equations for nonlocal operators. Zbl 1475.35155Grigor’yan, Alexander; Verbitsky, Igor 3 2020 Heat kernels and Besov spaces associated with second order divergence form elliptic operators. Zbl 1428.35148Cao, Jun; Grigor’yan, Alexander 2 2020 Path complexes and their homologies. Zbl 1448.05171Grigor’yan, A. A.; Lin, Yong; Muranov, Yu. V.; Yau, Shing-Tung 1 2020 Superlinear elliptic inequalities on manifolds. Zbl 1435.35169Grigor’yan, Alexander; Sun, Yuhua; Verbitsky, Igor 1 2020 Pointwise estimates of solutions to semilinear elliptic equations and inequalities. Zbl 1421.35073Grigor’yan, Alexander; Verbitsky, Igor 3 2019 On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds. Zbl 1430.58014Grigor’yan, Alexander; Sun, Yuhua 3 2019 Local and non-local Dirichlet forms on the Sierpiński carpet. Zbl 1426.28018Grigor’yan, Alexander; Yang, Meng 2 2019 Two-sided estimates of heat kernels of jump type Dirichlet forms. Zbl 1468.35081Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 11 2018 Introduction to analysis on graphs. Zbl 1416.05002Grigor’yan, Alexander 9 2018 On the path homology theory of digraphs and Eilenberg-Steenrod axioms. Zbl 1391.05125Grigor’yan, Alexander; Jimenez, Rolando; Muranov, Yuri; Yau, Shing-Tung 6 2018 Heat kernel estimates on connected sums of parabolic manifolds. Zbl 1388.35078Grigor’yan, Alexander; Ishiwata, Satoshi; Saloff-Coste, Laurent 5 2018 Path homology theory of multigraphs and quivers. Zbl 1404.55010Grigor’yan, Alexander; Muranov, Yuri; Vershinin, Vladimir; Yau, Shing-Tung 3 2018 Pointwise estimates for heat kernels of convolution-type operators. Zbl 06968912Grigor’yan, Alexander; Kondratiev, Yuri; Piatnitski, Andrey; Zhizhina, Elena 2 2018 Heat kernel estimates for an operator with a singular drift and isoperimetric inequalities. Zbl 1401.35145Grigor’yan, Alexander; Ouyang, Shunxiang; Röckner, Michael 2 2018 Determination of the walk dimension of the Sierpiński gasket without using diffusion. Zbl 1416.28011Grigor’yan, Alexander; Yang, Meng 1 2018 Existence of positive solutions to some nonlinear equations on locally finite graphs. Zbl 1384.34035Grigor’yan, Alexander; Lin, Yong; Yang, YunYan 17 2017 Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces. Zbl 1372.35123Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 9 2017 Homologies of digraphs and Künneth formulas. Zbl 1381.05062Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung 5 2017 Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula. Zbl 1387.60121Grigor’yan, Alexander; Kajino, Naotaka 4 2017 Yamabe type equations on graphs. Zbl 1351.35038Grigor’yan, Alexander; Lin, Yong; Yang, Yunyan 35 2016 Kazdan-Warner equation on graph. Zbl 1366.58006Grigor’yan, Alexander; Lin, Yong; Yang, Yunyan 31 2016 Surgery of the Faber-Krahn inequality and applications to heat kernel bounds. Zbl 1334.58019Grigor’yan, Alexander; Saloff-Coste, Laurent 10 2016 On a cohomology of digraphs and Hochschild cohomology. Zbl 1353.05056Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung 4 2016 A lower bound for the number of negative eigenvalues of Schrödinger operators. Zbl 1356.53044Grigor’yan, Alexander; Nadirashvili, Nikolai; Sire, Yannick 3 2016 Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces. Zbl 1331.35152Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 19 2015 Negative eigenvalues of two-dimensional Schrödinger operators. Zbl 1319.35128Grigor’yan, Alexander; Nadirashvili, Nikolai 9 2015 Heat kernel and Lipschitz-Besov spaces. Zbl 1327.35130Grigor’yan, Alexander; Liu, Liguang 8 2015 Cohomology of digraphs and (undirected) graphs. Zbl 1329.05132Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung 7 2015 On a class of random perturbations of the hierarchical Laplacian. Zbl 1448.47050Bendikov, Alexander D.; Grigor’yan, Alexander A.; Molchanov, Stanislav A.; Samorodnitsky, Gennady P. 3 2015 Upper bounds of heat kernels on doubling spaces. Zbl 06332192Grigor’yan, Alexander; Hu, Jiaxin 27 2014 Isotropic Markov semigroups on ultra-metric spaces. Zbl 1322.60151Bendikov, A. D.; Grigor’yan, A. A.; Pittet, Ch; Woess, W. 22 2014 On nonnegative solutions of the inequality \(\Delta u+u^{\sigma }\leq 0\) on Riemannian manifolds. Zbl 1296.58011Grigor’yan, Alexander; Sun, Yuhua 21 2014 Heat kernels and Green functions on metric measure spaces. Zbl 1293.35128Grigor’yan, Alexander; Hu, Jiaxin 20 2014 Estimates of heat kernels for non-local regular Dirichlet forms. Zbl 1304.47058Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 18 2014 Homotopy theory for digraphs. Zbl 1312.05063Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung 13 2014 Heat kernels on metric measure spaces. Zbl 1323.58018Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 9 2014 Graphs associated with simplicial complexes. Zbl 1297.05269Grigor’yan, A.; Muranov, Yu. V.; Yau, Shing-Tung 8 2014 Stochastic completeness of jump processes on metric measure spaces. Zbl 1318.28024Grigor’yan, Alexander; Huang, Xueping 1 2014 Parabolicity and stochastic completeness of manifolds in terms of the Green formula. Zbl 1356.58007Grigor’yan, Alexander; Masamune, Jun 20 2013 Stochastic completeness of symmetry Markov processes and volume growth. Zbl 1326.58020Grigor’yan, Alexander 3 2013 Two-sided estimates of heat kernels on metric measure spaces. Zbl 1252.35148Grigor’yan, Alexander; Telcs, Andras 49 2012 On the equivalence of parabolic Harnack inequalities and heat kernel estimates. Zbl 1281.58016Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi 38 2012 On stochastic completeness of jump processes. Zbl 1408.60076Grigor’yan, Alexander; Huang, Xueping; Masamune, Jun 32 2012 On a class of Markov semigroups on discrete ultra-metric spaces. Zbl 1260.60142Bendikov, Alexander; Grigor’yan, Alexander; Pittet, Christophe 10 2012 Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data. Zbl 1251.58009van den Berg, M.; Gilkey, Peter B.; Grigor’yan, A.; Kirsten, K. 5 2012 Comparison inequalities for heat semigroups and heat kernels on metric measure spaces. Zbl 1207.58021Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 16 2010 Heat kernels on metric measure spaces with regular volume growth. Zbl 1217.58018Grigor’yan, Alexander 10 2010 On the existence of positive solutions of semilinear elliptic inequalities on Riemannian manifolds. Zbl 1185.35344Grigor’yan, Alexander; Kondratiev, Vladimir A. 10 2010 Heat kernel and analysis on manifolds. Zbl 1206.58008Grigor’yan, Alexander 142 2009 Heat kernel upper bounds for jump processes and the first exit time. Zbl 1158.60039Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi 54 2009 Heat kernel on manifolds with ends. Zbl 1239.58016Grigor’yan, Alexander; Saloff-Coste, Laurent 25 2009 Heat kernels on metric spaces with doubling measure. Zbl 1197.35129Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 11 2009 Volume growth and escape rate of Brownian motion on a Cartan-Hadamard manifold. Zbl 1167.58019Grigor’yan, Alexander; Hsu, Elton 8 2009 Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces. Zbl 1154.47034Grigor’yan, Alexander; Hu, Jiaxin 26 2008 On the dichotomy in the heat kernel two sided estimates. Zbl 1162.47037Grigor’yan, Alexander; Kumagai, Takashi 15 2008 Lower estimates for a perturbed Green function. Zbl 1158.35022Grigor’yan, Alexander; Hansen, Wolfhard 8 2008 Obtaining upper bounds of heat kernels from lower bounds. Zbl 1148.58013Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 6 2008 Heat kernels on weighted manifolds and applications. Zbl 1106.58016Grigor’yan, Alexander 62 2006 Stability results for Harnack inequalities. Zbl 1115.58024Grigor’yan, Alexander; Saloff-Coste, Laurent 47 2005 The discrete integral maximum principle and its applications. Zbl 1096.60023Coulhon, Thierry; Grigor’yan, Alexander; Zucca, Fabio 19 2005 Eigenvalues of elliptic operators and geometric applications. Zbl 1061.58027Grigor’yan, Alexander; Netrusov, Yuri; Yau, Shing-Tung 20 2004 Surveys in differential geometry. Vol. IX: Eigenvalues of Laplacians and other geometric operators. Zbl 1050.53002 1 2004 Heat kernels on metric measure spaces and an application to semilinear elliptic equations. Zbl 1018.60075Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 55 2003 Heat kernels and function theory on metric measure spaces. Zbl 1048.58021Grigor’yan, Alexander 35 2003 On isoperimetric profiles of product spaces. Zbl 1085.53027Coulhon, Thierry; Grigor’yan, Alexander; Levin, Daniel 12 2003 Isoperimetric properties of higher eigenvalues of elliptic operators. Zbl 1042.58017Grigor’yan, Alexander; Yau, Shing-Tung 11 2003 Pointwise estimates for transition probabilities of random walks on infinite graphs. Zbl 1048.60081Coulhon, Thierry; Grigor’yan, Alexander 4 2003 Heat kernels and analysis on manifolds, graphs, and metric spaces. Lecture notes from a quarter program on heat kernels, random walks, and analysis on manifolds and graphs, April 16–July 13, 2002, Paris, France. Zbl 1029.00030 3 2003 Recurrence and transience of branching diffusion processes on Riemannian manifolds. Zbl 1014.60081Grigor’yan, Alexander; Kelbert, Mark 2 2003 Harnack inequalities and sub-Gaussian estimates for random walks. Zbl 1011.60021Grigor’yan, A.; Telcs, A. 40 2002 Dirichlet heat kernel in the exterior of a compact set. Zbl 1037.58018Grigor’yan, Alexander; Saloff-Coste, Laurent 31 2002 Hitting probabilities for Brownian motion on Riemannian manifolds. Zbl 1042.58022Grigor’yan, Alexander; Saloff-Coste, Laurent 20 2002 Sub-Gaussian estimates of heat kernels on infinite graphs. Zbl 1010.35016Grigor’yan, Alexander; Telcs, Andras 41 2001 Manifolds and graphs with slow heat kernel decay. Zbl 1003.58025Barlow, Martin; Coulhon, Thierry; Grigor’yan, Alexander 32 2001 A geometric approach to on-diagonal heat kernel lower bounds on groups. Zbl 1137.58307Coulhon, Thierry; Grigor’yan, Alexander; Pittet, Christophe 21 2001 Heat kernels on manifolds, graphs and fractals. Zbl 1057.58010Grigor’yan, Alexander 1 2001 XIIIth international congress on mathematical physics. Proceedings of the ICMP 2000, Imperial College, London, Great Britain, July 17–22, 2000. Zbl 0994.00023 1 2001 Asymptotic separation for independent trajectories of Markov processes. Zbl 0973.58020Grigor’yan, Alexander; Kelbert, Mark 1 2001 Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs. Zbl 1001.58022Chung, Fan; Grigor’yan, Alexander; Yau, Shing-Tung 22 2000 On Hardy-Littlewood inequality for Brownian motion on Riemannian manifolds. Zbl 1026.58028Grigor’yan, Alexander; Kelbert, Mark 7 2000 Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds. Zbl 0927.58019Grigor’yan, Alexander 298 1999 Estimates of heat kernels on Riemannian manifolds. Zbl 0985.58007Grigor’yan, Alexander 40 1999 Escape rate of Brownian motion on Riemannian manifolds. Zbl 1020.58024Grigor’yan, Alexander 21 1999 Isoperimetric inequalities and capacities on Riemannian manifolds. Zbl 0947.58034Grigor’yan, Alexander 12 1999 Heat kernel on connected sums of Riemannian manifolds. Zbl 0957.58023Grigor’yan, Alexander; Saloff-Coste, Laurent 11 1999 Decomposition of a metric space by capacitors. Zbl 0976.31006Grigor’yan, A.; Yau, S.-T. 8 1999 Random walks on graphs with regular volume growth. Zbl 0918.60053Coulhon, T.; Grigoryan, A. 46 1998 A Liouville property for Schrödinger operators. Zbl 0938.31007Grigor’yan, Alexander; Hansen, Wolfhard 21 1998 The heat kernel of hyperbolic space. Zbl 0921.58063Grigor’yan, Alexander; Noguchi, Masakazu 21 1998 Range of fluctuation of Brownian motion on a complete Riemannian manifold. Zbl 0934.58023Grigor’yan, Alexander; Kelbert, Mark 11 1998 Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds. Zbl 0865.58042Grigor’yan, Alexander 59 1997 On-diagonal lower bounds for heat kernels and Markov chains. Zbl 0920.58064Coulhon, Thierry; Grigor’yan, Alexander 34 1997 Eigenvalues and diameters for manifolds and graphs. Zbl 0890.58093Chung, F. R. K.; Grigor’yan, A.; Yau, S.-T. 6 1997 Upper bounds for eigenvalues of the discrete and continuous Laplace operators. Zbl 0844.53029Chung, F. R. K.; Grigor’yan, A.; Yau, Shing-Tung 20 1996 Heat kernels, volume growth and anti-isoperimetric inequalities. Zbl 0873.58062Coulhon, Thierry; Grigor’yan, Alexander 3 1996 Upper bounds of derivatives of the heat kernel on an arbitrary complete manifold. Zbl 0842.58070Grigor’yan, Alexander 31 1995 Heat kernel of a noncompact Riemannian manifold. Zbl 0829.58041Grigor’yan, Alexander 6 1995 Heat kernel upper bounds on a complete non-compact manifold. Zbl 0810.58040Grigor’yan, Alexander 65 1994 Integral maximum principle and its applications. Zbl 0812.58082Grigor’yan, Alexander 18 1994 ...and 21 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,249 Authors 48 Grigor’yan, Alexander Asaturovich 29 Kumagai, Takashi 28 Punzo, Fabio 28 Saloff-Coste, Laurent 19 Chen, Zhen-Qing 16 Coulhon, Thierry 16 Hua, Bobo 16 Palmer, Vicente 16 Wang, Jian 15 Barlow, Martin T. 15 Hu, Jiaxin 14 de Lima, Henrique F. 14 Keller, Matthias 14 Lin, Yong 13 Grillo, Gabriele 13 Pigola, Stefano 13 Rigoli, Marco 13 Teplyaev, Alexander 12 Bendikov, Alexander D. 11 Muratori, Matteo 11 Setti, Alberto G. 11 Sun, Yuhua 10 Lau, Kasing 10 Masamune, Jun 10 Ouhabaz, El Maati 10 Telcs, András 9 Alías, Luis J. 9 Bernicot, Frédéric 9 Duong, Xuan Thinh 9 Gimeno, Vicent 9 Huang, Xueping 9 Yau, Shing-Tung 8 Carron, Gilles 8 Kim, Panki 8 Lenz, Daniel H. 8 Mari, Luciano 8 Mazepa, Elena Alekseevna 8 Murugan, Mathav Kishore 8 Bessa, Gregório Pacelli 8 Pittet, Christophe 8 Shanmugalingam, Nageswari 8 Velásquez, Marco Antonio Lázaro 8 Wojciechowski, Radosław Krzysztof 8 Yan, Lixin 8 Yang, Dachun 8 Zheng, Tianyi 7 Bass, Richard F. 7 Ge, Huabin 7 Holopainen, Ilkka 7 Markvorsen, Steen 7 Mhaskar, Hrushikesh N. 7 Schmidt, Marcel 7 Shiozawa, Yuichi 7 Sikora, Adam S. 7 The Anh Bui 7 Wang, Feng-Yu 7 Wu, Yiting 6 Alonso-Ruiz, Patricia 6 Auscher, Pascal 6 Colbois, Bruno 6 Cunha, Antonio W. 6 Güneysu, Batu 6 Hansen, Wolfhard 6 Hurtado, Ana 6 Ishige, Kazuhiro 6 Jost, Jürgen 6 Losev, Alexander Georgievoch 6 Monticelli, Dario Daniele 6 Münch, Florentin 6 Muranov, Yuriĭ Vladimirovich 6 Murata, Minoru 6 Rogers, Luke G. 6 Russ, Emmanuel 6 Takeda, Masayoshi 6 Tian, Canrong 6 van den Berg, Michiel 6 Verbitsky, Igor E. 5 Atsuji, Atsushi 5 Badr, Nadine 5 Bailleul, Ismaël F. 5 Baudoin, Fabrice 5 de Lima, Eudes Leite 5 Devyver, Baptiste 5 Dshalalow, Jewgeni H. 5 Frey, Dorothee 5 Grzywny, Tomasz 5 Gu, Qingsong 5 Kajino, Naotaka 5 Lierl, Janna 5 Milatovic, Ognjen 5 Robinson, Derek W. 5 Rosales, César 4 Albujer, Alma L. 4 Berchio, Elvise 4 Bogdan, Krzysztof 4 Chen, Peng 4 Chen, Xin 4 Colli, Pierluigi 4 Erschler, Anna 4 Feneuil, Joseph ...and 1,149 more Authors all top 5 Cited in 259 Serials 77 Journal of Functional Analysis 55 Potential Analysis 53 Journal of Mathematical Analysis and Applications 49 The Journal of Geometric Analysis 45 Transactions of the American Mathematical Society 30 Proceedings of the American Mathematical Society 28 Advances in Mathematics 28 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 27 Journal of Differential Equations 27 Mathematische Zeitschrift 27 Calculus of Variations and Partial Differential Equations 26 Journal de Mathématiques Pures et Appliquées. Neuvième Série 25 The Annals of Probability 22 Mathematische Annalen 18 Revista Matemática Iberoamericana 15 Annales de l’Institut Fourier 15 Annals of Global Analysis and Geometry 14 Journal of Geometry and Physics 14 Journal für die Reine und Angewandte Mathematik 14 Probability Theory and Related Fields 14 Stochastic Processes and their Applications 13 Journal of Theoretical Probability 13 Differential Geometry and its Applications 12 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 12 Journal of Evolution Equations 11 Forum Mathematicum 10 Annali di Matematica Pura ed Applicata. 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English Series 4 Journal of High Energy Physics 4 Annales Henri Poincaré 4 Analysis and Geometry in Metric Spaces 4 Open Mathematics 4 Annales Fennici Mathematici 3 Discrete Applied Mathematics 3 Rocky Mountain Journal of Mathematics 3 Bulletin of the London Mathematical Society 3 Collectanea Mathematica 3 Integral Equations and Operator Theory 3 Journal of Approximation Theory 3 Journal of the Korean Mathematical Society 3 Quaestiones Mathematicae 3 Semigroup Forum 3 European Journal of Combinatorics 3 Acta Applicandae Mathematicae 3 The Annals of Applied Probability 3 Geometric and Functional Analysis. GAFA 3 Bulletin of the American Mathematical Society. New Series 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Electronic Journal of Probability 3 Bernoulli 3 Discrete and Continuous Dynamical Systems 3 Mathematical Physics, Analysis and Geometry 3 Positivity 3 Annals of Mathematics. Second Series 3 Differential Equations 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 Mediterranean Journal of Mathematics 3 Journal of Pseudo-Differential Operators and Applications 3 Advances in Nonlinear Analysis 3 Journal de l’École Polytechnique – Mathématiques 2 Bulletin of the Australian Mathematical Society ...and 159 more Serials all top 5 Cited in 53 Fields 497 Partial differential equations (35-XX) 385 Global analysis, analysis on manifolds (58-XX) 358 Probability theory and stochastic processes (60-XX) 294 Differential geometry (53-XX) 166 Potential theory (31-XX) 155 Operator theory (47-XX) 107 Combinatorics (05-XX) 93 Harmonic analysis on Euclidean spaces (42-XX) 87 Functional analysis (46-XX) 59 Measure and integration (28-XX) 43 Statistical mechanics, structure of matter (82-XX) 37 Quantum theory (81-XX) 36 Calculus of variations and optimal control; optimization (49-XX) 35 Functions of a complex variable (30-XX) 34 Abstract harmonic analysis (43-XX) 26 Real functions (26-XX) 25 Group theory and generalizations (20-XX) 23 Ordinary differential equations (34-XX) 22 Several complex variables and analytic spaces (32-XX) 19 Topological groups, Lie groups (22-XX) 19 Difference and functional equations (39-XX) 18 Relativity and gravitational theory (83-XX) 14 Algebraic topology (55-XX) 14 Manifolds and cell complexes (57-XX) 13 Dynamical systems and ergodic theory (37-XX) 11 Fluid mechanics (76-XX) 11 Biology and other natural sciences (92-XX) 10 Number theory (11-XX) 9 Statistics (62-XX) 8 Approximations and expansions (41-XX) 8 Convex and discrete geometry (52-XX) 8 Numerical analysis (65-XX) 8 Information and communication theory, circuits (94-XX) 7 Algebraic geometry (14-XX) 7 Geometry (51-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Integral equations (45-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Computer science (68-XX) 4 General and overarching topics; collections (00-XX) 4 Category theory; homological algebra (18-XX) 4 Integral transforms, operational calculus (44-XX) 4 General topology (54-XX) 4 Mechanics of deformable solids (74-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Special functions (33-XX) 2 Operations research, mathematical programming (90-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 \(K\)-theory (19-XX) 1 Optics, electromagnetic theory (78-XX) Citations by Year