## Grigor’yan, Alexander Asaturovich

Compute Distance To:
 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
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### 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
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### 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)

### 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 0927.58019
Grigor’yan, Alexander
1999
Heat kernel and analysis on manifolds. Zbl 1206.58008
Grigor’yan, Alexander
2009
Heat kernel upper bounds on a complete non-compact manifold. Zbl 0810.58040
Grigor’yan, Alexander
1994
Heat kernels on weighted manifolds and applications. Zbl 1106.58016
Grigor’yan, Alexander
2006
Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds. Zbl 0865.58042
Grigor’yan, Alexander
1997
Heat kernels on metric measure spaces and an application to semilinear elliptic equations. Zbl 1018.60075
Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2003
Heat kernel upper bounds for jump processes and the first exit time. Zbl 1158.60039
Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi
2009
Two-sided estimates of heat kernels on metric measure spaces. Zbl 1252.35148
Grigor’yan, Alexander; Telcs, Andras
2012
Stability results for Harnack inequalities. Zbl 1115.58024
Grigor’yan, Alexander; Saloff-Coste, Laurent
2005
Random walks on graphs with regular volume growth. Zbl 0918.60053
Coulhon, T.; Grigoryan, A.
1998
Sub-Gaussian estimates of heat kernels on infinite graphs. Zbl 1010.35016
Grigor’yan, Alexander; Telcs, Andras
2001
Harnack inequalities and sub-Gaussian estimates for random walks. Zbl 1011.60021
Grigor’yan, A.; Telcs, A.
2002
Estimates of heat kernels on Riemannian manifolds. Zbl 0985.58007
Grigor’yan, Alexander
1999
The heat equation on noncompact Riemannian manifolds. Zbl 0776.58035
Grigor’yan, A. A.
1992
On the equivalence of parabolic Harnack inequalities and heat kernel estimates. Zbl 1281.58016
Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi
2012
Heat equation on noncompact Riemannian manifolds. Zbl 0743.58031
Grigor’yan, A. A.
1991
On stochastically complete manifolds. Zbl 0632.58041
Grigor’yan, A. A.
1987
Heat kernels and function theory on metric measure spaces. Zbl 1048.58021
Grigor’yan, Alexander
2003
Yamabe type equations on graphs. Zbl 1351.35038
Grigor’yan, Alexander; Lin, Yong; Yang, Yunyan
2016
On-diagonal lower bounds for heat kernels and Markov chains. Zbl 0920.58064
Coulhon, Thierry; Grigor’yan, Alexander
1997
On stochastic completeness of jump processes. Zbl 1408.60076
Grigor’yan, Alexander; Huang, Xueping; Masamune, Jun
2012
Manifolds and graphs with slow heat kernel decay. Zbl 1003.58025
Barlow, Martin; Coulhon, Thierry; Grigor’yan, Alexander
2001
Dirichlet heat kernel in the exterior of a compact set. Zbl 1037.58018
Grigor’yan, Alexander; Saloff-Coste, Laurent
2002
Kazdan-Warner equation on graph. Zbl 1366.58006
Grigor’yan, Alexander; Lin, Yong; Yang, Yunyan
2016
Upper bounds of derivatives of the heat kernel on an arbitrary complete manifold. Zbl 0842.58070
Grigor’yan, Alexander
1995
Upper bounds of heat kernels on doubling spaces. Zbl 06332192
Grigor’yan, Alexander; Hu, Jiaxin
2014
Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces. Zbl 1154.47034
Grigor’yan, Alexander; Hu, Jiaxin
2008
Heat kernel on manifolds with ends. Zbl 1239.58016
Grigor’yan, Alexander; Saloff-Coste, Laurent
2009
Isotropic Markov semigroups on ultra-metric spaces. Zbl 1322.60151
Bendikov, A. D.; Grigor’yan, A. A.; Pittet, Ch; Woess, W.
2014
Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs. Zbl 1001.58022
Chung, Fan; Grigor’yan, Alexander; Yau, Shing-Tung
2000
On the existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds. Zbl 0612.31007
Grigor’yan, A. A.
1987
On nonnegative solutions of the inequality $$\Delta u+u^{\sigma }\leq 0$$ on Riemannian manifolds. Zbl 1296.58011
Grigor’yan, Alexander; Sun, Yuhua
2014
A Liouville property for Schrödinger operators. Zbl 0938.31007
Grigor’yan, Alexander; Hansen, Wolfhard
1998
A geometric approach to on-diagonal heat kernel lower bounds on groups. Zbl 1137.58307
Coulhon, Thierry; Grigor’yan, Alexander; Pittet, Christophe
2001
The heat kernel of hyperbolic space. Zbl 0921.58063
Grigor’yan, Alexander; Noguchi, Masakazu
1998
Escape rate of Brownian motion on Riemannian manifolds. Zbl 1020.58024
Grigor’yan, Alexander
1999
Parabolicity and stochastic completeness of manifolds in terms of the Green formula. Zbl 1356.58007
Grigor’yan, Alexander; Masamune, Jun
2013
Eigenvalues of elliptic operators and geometric applications. Zbl 1061.58027
Grigor’yan, Alexander; Netrusov, Yuri; Yau, Shing-Tung
2004
Heat kernels and Green functions on metric measure spaces. Zbl 1293.35128
Grigor’yan, Alexander; Hu, Jiaxin
2014
Upper bounds for eigenvalues of the discrete and continuous Laplace operators. Zbl 0844.53029
Chung, F. R. K.; Grigor’yan, A.; Yau, Shing-Tung
1996
Hitting probabilities for Brownian motion on Riemannian manifolds. Zbl 1042.58022
Grigor’yan, Alexander; Saloff-Coste, Laurent
2002
The discrete integral maximum principle and its applications. Zbl 1096.60023
Coulhon, Thierry; Grigor’yan, Alexander; Zucca, Fabio
2005
Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces. Zbl 1331.35152
Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2015
Estimates of heat kernels for non-local regular Dirichlet forms. Zbl 1304.47058
Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2014
Integral maximum principle and its applications. Zbl 0812.58082
Grigor’yan, Alexander
1994
Existence of positive solutions to some nonlinear equations on locally finite graphs. Zbl 1384.34035
Grigor’yan, Alexander; Lin, Yong; Yang, YunYan
2017
Comparison inequalities for heat semigroups and heat kernels on metric measure spaces. Zbl 1207.58021
Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2010
On the dichotomy in the heat kernel two sided estimates. Zbl 1162.47037
Grigor’yan, Alexander; Kumagai, Takashi
2008
Stochastically complete manifolds and summable harmonic functions. Zbl 0677.60086
Grigor’yan, A. A.
1989
Homotopy theory for digraphs. Zbl 1312.05063
Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung
2014
Existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds. Zbl 0596.31004
Grigor’yan, A. A.
1985
Isoperimetric inequalities and capacities on Riemannian manifolds. Zbl 0947.58034
Grigor’yan, Alexander
1999
On isoperimetric profiles of product spaces. Zbl 1085.53027
Coulhon, Thierry; Grigor’yan, Alexander; Levin, Daniel
2003
Range of fluctuation of Brownian motion on a complete Riemannian manifold. Zbl 0934.58023
Grigor’yan, Alexander; Kelbert, Mark
1998
Heat kernels on metric spaces with doubling measure. Zbl 1197.35129
Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2009
Isoperimetric properties of higher eigenvalues of elliptic operators. Zbl 1042.58017
Grigor’yan, Alexander; Yau, Shing-Tung
2003
Two-sided estimates of heat kernels of jump type Dirichlet forms. Zbl 1468.35081
Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin
2018
Heat kernel on connected sums of Riemannian manifolds. Zbl 0957.58023
Grigor’yan, Alexander; Saloff-Coste, Laurent
1999
Heat kernels on metric measure spaces with regular volume growth. Zbl 1217.58018
Grigor’yan, Alexander
2010
On a class of Markov semigroups on discrete ultra-metric spaces. Zbl 1260.60142
Bendikov, Alexander; Grigor’yan, Alexander; Pittet, Christophe
2012
On the existence of positive solutions of semilinear elliptic inequalities on Riemannian manifolds. Zbl 1185.35344
Grigor’yan, Alexander; Kondratiev, Vladimir A.
2010
On the existence of a Green’s function on a manifold. Zbl 0542.35025
Grigor’yan, A. A.
1983
Surgery of the Faber-Krahn inequality and applications to heat kernel bounds. Zbl 1334.58019
Grigor’yan, Alexander; Saloff-Coste, Laurent
2016
Heat kernel on a manifold with a local Harnack inequality. Zbl 0845.58056
Grigor’yan, Alexander
1994
Heat kernels on metric measure spaces. Zbl 1323.58018
Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2014
Negative eigenvalues of two-dimensional Schrödinger operators. Zbl 1319.35128
Grigor’yan, Alexander; Nadirashvili, Nikolai
2015
Introduction to analysis on graphs. Zbl 1416.05002
Grigor’yan, Alexander
2018
Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces. Zbl 1372.35123
Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin
2017
Volume growth and escape rate of Brownian motion on a Cartan-Hadamard manifold. Zbl 1167.58019
Grigor’yan, Alexander; Hsu, Elton
2009
Lower estimates for a perturbed Green function. Zbl 1158.35022
Grigor’yan, Alexander; Hansen, Wolfhard
2008
Graphs associated with simplicial complexes. Zbl 1297.05269
Grigor’yan, A.; Muranov, Yu. V.; Yau, Shing-Tung
2014
Heat kernel and Lipschitz-Besov spaces. Zbl 1327.35130
Grigor’yan, Alexander; Liu, Liguang
2015
Decomposition of a metric space by capacitors. Zbl 0976.31006
Grigor’yan, A.; Yau, S.-T.
1999
On Hardy-Littlewood inequality for Brownian motion on Riemannian manifolds. Zbl 1026.58028
Grigor’yan, Alexander; Kelbert, Mark
2000
Cohomology of digraphs and (undirected) graphs. Zbl 1329.05132
Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung
2015
Liouville theorems and external boundary value problems. Zbl 0639.58029
Grigor’yan, A. A.; Nadirashvili, N. S.
1987
Stochastically complete manifolds and summable harmonic functions. Zbl 0661.60090
Grigoryan, A. A.
1988
Obtaining upper bounds of heat kernels from lower bounds. Zbl 1148.58013
Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2008
Dimension of spaces of harmonic functions. Zbl 0721.31003
Grigor’yan, A. A.
1990
Eigenvalues and diameters for manifolds and graphs. Zbl 0890.58093
Chung, F. R. K.; Grigor’yan, A.; Yau, S.-T.
1997
On the path homology theory of digraphs and Eilenberg-Steenrod axioms. Zbl 1391.05125
Grigor’yan, Alexander; Jimenez, Rolando; Muranov, Yuri; Yau, Shing-Tung
2018
Heat kernel of a noncompact Riemannian manifold. Zbl 0829.58041
Grigor’yan, Alexander
1995
On Liouville theorems for harmonic functions with finite Dirichlet integral. Zbl 0646.31009
Grigor’yan, A. A.
1987
Bounded solutions of the Schrödinger equation on noncompact Riemannian manifolds. Zbl 0744.58070
Grigor’yan, A. A.
1989
Gaussian upper bounds for the heat kernel and for its derivatives on a Riemannian manifold. Zbl 0885.58088
Grigor’yan, A.
1994
Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data. Zbl 1251.58009
van den Berg, M.; Gilkey, Peter B.; Grigor’yan, A.; Kirsten, K.
2012
Heat kernel estimates on connected sums of parabolic manifolds. Zbl 1388.35078
Grigor’yan, Alexander; Ishiwata, Satoshi; Saloff-Coste, Laurent
2018
Homologies of digraphs and Künneth formulas. Zbl 1381.05062
Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung
2017
Isoperimetric inequalities for Riemannian products. Zbl 0599.53035
Grigor’yan, A. A.
1985
Pointwise estimates for transition probabilities of random walks on infinite graphs. Zbl 1048.60081
Coulhon, Thierry; Grigor’yan, Alexander
2003
On a cohomology of digraphs and Hochschild cohomology. Zbl 1353.05056
Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung
2016
Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula. Zbl 1387.60121
Grigor’yan, Alexander; Kajino, Naotaka
2017
Heat kernels, volume growth and anti-isoperimetric inequalities. Zbl 0873.58062
Coulhon, Thierry; Grigor’yan, Alexander
1996
A lower bound for the number of negative eigenvalues of Schrödinger operators. Zbl 1356.53044
Grigor’yan, Alexander; Nadirashvili, Nikolai; Sire, Yannick
2016
Stochastic completeness of symmetry Markov processes and volume growth. Zbl 1326.58020
Grigor’yan, Alexander
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
2003
On a class of random perturbations of the hierarchical Laplacian. Zbl 1448.47050
Bendikov, Alexander D.; Grigor’yan, Alexander A.; Molchanov, Stanislav A.; Samorodnitsky, Gennady P.
2015
Path homology theory of multigraphs and quivers. Zbl 1404.55010
Grigor’yan, Alexander; Muranov, Yuri; Vershinin, Vladimir; Yau, Shing-Tung
2018
Pointwise estimates of solutions to semilinear elliptic equations and inequalities. Zbl 1421.35073
Grigor’yan, Alexander; Verbitsky, Igor
2019
On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds. Zbl 1430.58014
Grigor’yan, Alexander; Sun, Yuhua
2019
The pointwise existence and properties of heat kernel. Zbl 1476.35114
Grigor&rsquo;yan, Alexander; Hu, Eryan; Hu, Jiaxin
2021
Pointwise estimates of solutions to nonlinear equations for nonlocal operators. Zbl 1475.35155
Grigor&rsquo;yan, Alexander; Verbitsky, Igor
2020
Heat kernels and Besov spaces associated with second order divergence form elliptic operators. Zbl 1428.35148
Cao, Jun; Grigor&rsquo;yan, Alexander
2020
Path complexes and their homologies. Zbl 1448.05171
Grigor&rsquo;yan, A. A.; Lin, Yong; Muranov, Yu. V.; Yau, Shing-Tung
2020
Superlinear elliptic inequalities on manifolds. Zbl 1435.35169
Grigor&rsquo;yan, Alexander; Sun, Yuhua; Verbitsky, Igor
2020
Pointwise estimates of solutions to semilinear elliptic equations and inequalities. Zbl 1421.35073
Grigor&rsquo;yan, Alexander; Verbitsky, Igor
2019
On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds. Zbl 1430.58014
Grigor&rsquo;yan, Alexander; Sun, Yuhua
2019
Local and non-local Dirichlet forms on the Sierpiński carpet. Zbl 1426.28018
Grigor&rsquo;yan, Alexander; Yang, Meng
2019
Two-sided estimates of heat kernels of jump type Dirichlet forms. Zbl 1468.35081
Grigor&rsquo;yan, Alexander; Hu, Eryan; Hu, Jiaxin
2018
Introduction to analysis on graphs. Zbl 1416.05002
Grigor&rsquo;yan, Alexander
2018
On the path homology theory of digraphs and Eilenberg-Steenrod axioms. Zbl 1391.05125
Grigor&rsquo;yan, Alexander; Jimenez, Rolando; Muranov, Yuri; Yau, Shing-Tung
2018
Heat kernel estimates on connected sums of parabolic manifolds. Zbl 1388.35078
Grigor&rsquo;yan, Alexander; Ishiwata, Satoshi; Saloff-Coste, Laurent
2018
Path homology theory of multigraphs and quivers. Zbl 1404.55010
Grigor&rsquo;yan, Alexander; Muranov, Yuri; Vershinin, Vladimir; Yau, Shing-Tung
2018
Pointwise estimates for heat kernels of convolution-type operators. Zbl 06968912
Grigor&rsquo;yan, Alexander; Kondratiev, Yuri; Piatnitski, Andrey; Zhizhina, Elena
2018
Heat kernel estimates for an operator with a singular drift and isoperimetric inequalities. Zbl 1401.35145
Grigor&rsquo;yan, Alexander; Ouyang, Shunxiang; Röckner, Michael
2018
Determination of the walk dimension of the Sierpiński gasket without using diffusion. Zbl 1416.28011
Grigor&rsquo;yan, Alexander; Yang, Meng
2018
Existence of positive solutions to some nonlinear equations on locally finite graphs. Zbl 1384.34035
Grigor&rsquo;yan, Alexander; Lin, Yong; Yang, YunYan
2017
Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces. Zbl 1372.35123
Grigor&rsquo;yan, Alexander; Hu, Eryan; Hu, Jiaxin
2017
Homologies of digraphs and Künneth formulas. Zbl 1381.05062
Grigor&rsquo;yan, Alexander; Muranov, Yuri; Yau, Shing-Tung
2017
Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula. Zbl 1387.60121
Grigor&rsquo;yan, Alexander; Kajino, Naotaka
2017
Yamabe type equations on graphs. Zbl 1351.35038
Grigor&rsquo;yan, Alexander; Lin, Yong; Yang, Yunyan
2016
Kazdan-Warner equation on graph. Zbl 1366.58006
Grigor&rsquo;yan, Alexander; Lin, Yong; Yang, Yunyan
2016
Surgery of the Faber-Krahn inequality and applications to heat kernel bounds. Zbl 1334.58019
Grigor&rsquo;yan, Alexander; Saloff-Coste, Laurent
2016
On a cohomology of digraphs and Hochschild cohomology. Zbl 1353.05056
Grigor&rsquo;yan, Alexander; Muranov, Yuri; Yau, Shing-Tung
2016
A lower bound for the number of negative eigenvalues of Schrödinger operators. Zbl 1356.53044
Grigor&rsquo;yan, Alexander; Nadirashvili, Nikolai; Sire, Yannick
2016
Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces. Zbl 1331.35152
Grigor&rsquo;yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2015
Negative eigenvalues of two-dimensional Schrödinger operators. Zbl 1319.35128
Grigor&rsquo;yan, Alexander; Nadirashvili, Nikolai
2015
Heat kernel and Lipschitz-Besov spaces. Zbl 1327.35130
Grigor&rsquo;yan, Alexander; Liu, Liguang
2015
Cohomology of digraphs and (undirected) graphs. Zbl 1329.05132
Grigor&rsquo;yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung
2015
On a class of random perturbations of the hierarchical Laplacian. Zbl 1448.47050
Bendikov, Alexander D.; Grigor&rsquo;yan, Alexander A.; Molchanov, Stanislav A.; Samorodnitsky, Gennady P.
2015
Upper bounds of heat kernels on doubling spaces. Zbl 06332192
Grigor&rsquo;yan, Alexander; Hu, Jiaxin
2014
Isotropic Markov semigroups on ultra-metric spaces. Zbl 1322.60151
Bendikov, A. D.; Grigor&rsquo;yan, A. A.; Pittet, Ch; Woess, W.
2014
On nonnegative solutions of the inequality $$\Delta u+u^{\sigma }\leq 0$$ on Riemannian manifolds. Zbl 1296.58011
Grigor&rsquo;yan, Alexander; Sun, Yuhua
2014
Heat kernels and Green functions on metric measure spaces. Zbl 1293.35128
Grigor&rsquo;yan, Alexander; Hu, Jiaxin
2014
Estimates of heat kernels for non-local regular Dirichlet forms. Zbl 1304.47058
Grigor&rsquo;yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2014
Homotopy theory for digraphs. Zbl 1312.05063
Grigor&rsquo;yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung
2014
Heat kernels on metric measure spaces. Zbl 1323.58018
Grigor&rsquo;yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2014
Graphs associated with simplicial complexes. Zbl 1297.05269
Grigor&rsquo;yan, A.; Muranov, Yu. V.; Yau, Shing-Tung
2014
Stochastic completeness of jump processes on metric measure spaces. Zbl 1318.28024
Grigor&rsquo;yan, Alexander; Huang, Xueping
2014
Parabolicity and stochastic completeness of manifolds in terms of the Green formula. Zbl 1356.58007
Grigor&rsquo;yan, Alexander; Masamune, Jun
2013
Stochastic completeness of symmetry Markov processes and volume growth. Zbl 1326.58020
Grigor&rsquo;yan, Alexander
2013
Two-sided estimates of heat kernels on metric measure spaces. Zbl 1252.35148
Grigor&rsquo;yan, Alexander; Telcs, Andras
2012
On the equivalence of parabolic Harnack inequalities and heat kernel estimates. Zbl 1281.58016
Barlow, Martin T.; Grigor&rsquo;yan, Alexander; Kumagai, Takashi
2012
On stochastic completeness of jump processes. Zbl 1408.60076
Grigor&rsquo;yan, Alexander; Huang, Xueping; Masamune, Jun
2012
On a class of Markov semigroups on discrete ultra-metric spaces. Zbl 1260.60142
Bendikov, Alexander; Grigor&rsquo;yan, Alexander; Pittet, Christophe
2012
Hardy inequality and heat semigroup estimates for Riemannian manifolds with singular data. Zbl 1251.58009
van den Berg, M.; Gilkey, Peter B.; Grigor&rsquo;yan, A.; Kirsten, K.
2012
Comparison inequalities for heat semigroups and heat kernels on metric measure spaces. Zbl 1207.58021
Grigor&rsquo;yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2010
Heat kernels on metric measure spaces with regular volume growth. Zbl 1217.58018
Grigor&rsquo;yan, Alexander
2010
On the existence of positive solutions of semilinear elliptic inequalities on Riemannian manifolds. Zbl 1185.35344
Grigor&rsquo;yan, Alexander; Kondratiev, Vladimir A.
2010
Heat kernel and analysis on manifolds. Zbl 1206.58008
Grigor&rsquo;yan, Alexander
2009
Heat kernel upper bounds for jump processes and the first exit time. Zbl 1158.60039
Barlow, Martin T.; Grigor&rsquo;yan, Alexander; Kumagai, Takashi
2009
Heat kernel on manifolds with ends. Zbl 1239.58016
Grigor&rsquo;yan, Alexander; Saloff-Coste, Laurent
2009
Heat kernels on metric spaces with doubling measure. Zbl 1197.35129
Grigor&rsquo;yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2009
Volume growth and escape rate of Brownian motion on a Cartan-Hadamard manifold. Zbl 1167.58019
Grigor&rsquo;yan, Alexander; Hsu, Elton
2009
Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces. Zbl 1154.47034
Grigor&rsquo;yan, Alexander; Hu, Jiaxin
2008
On the dichotomy in the heat kernel two sided estimates. Zbl 1162.47037
Grigor&rsquo;yan, Alexander; Kumagai, Takashi
2008
Lower estimates for a perturbed Green function. Zbl 1158.35022
Grigor&rsquo;yan, Alexander; Hansen, Wolfhard
2008
Obtaining upper bounds of heat kernels from lower bounds. Zbl 1148.58013
Grigor&rsquo;yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2008
Heat kernels on weighted manifolds and applications. Zbl 1106.58016
Grigor&rsquo;yan, Alexander
2006
Stability results for Harnack inequalities. Zbl 1115.58024
Grigor&rsquo;yan, Alexander; Saloff-Coste, Laurent
2005
The discrete integral maximum principle and its applications. Zbl 1096.60023
Coulhon, Thierry; Grigor&rsquo;yan, Alexander; Zucca, Fabio
2005
Eigenvalues of elliptic operators and geometric applications. Zbl 1061.58027
Grigor&rsquo;yan, Alexander; Netrusov, Yuri; Yau, Shing-Tung
2004
Surveys in differential geometry. Vol. IX: Eigenvalues of Laplacians and other geometric operators. Zbl 1050.53002
2004
Heat kernels on metric measure spaces and an application to semilinear elliptic equations. Zbl 1018.60075
Grigor&rsquo;yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing
2003
Heat kernels and function theory on metric measure spaces. Zbl 1048.58021
Grigor&rsquo;yan, Alexander
2003
On isoperimetric profiles of product spaces. Zbl 1085.53027
Coulhon, Thierry; Grigor&rsquo;yan, Alexander; Levin, Daniel
2003
Isoperimetric properties of higher eigenvalues of elliptic operators. Zbl 1042.58017
Grigor&rsquo;yan, Alexander; Yau, Shing-Tung
2003
Pointwise estimates for transition probabilities of random walks on infinite graphs. Zbl 1048.60081
Coulhon, Thierry; Grigor&rsquo;yan, Alexander
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
2003
Recurrence and transience of branching diffusion processes on Riemannian manifolds. Zbl 1014.60081
Grigor&rsquo;yan, Alexander; Kelbert, Mark
2003
Harnack inequalities and sub-Gaussian estimates for random walks. Zbl 1011.60021
Grigor&rsquo;yan, A.; Telcs, A.
2002
Dirichlet heat kernel in the exterior of a compact set. Zbl 1037.58018
Grigor&rsquo;yan, Alexander; Saloff-Coste, Laurent
2002
Hitting probabilities for Brownian motion on Riemannian manifolds. Zbl 1042.58022
Grigor&rsquo;yan, Alexander; Saloff-Coste, Laurent
2002
Sub-Gaussian estimates of heat kernels on infinite graphs. Zbl 1010.35016
Grigor&rsquo;yan, Alexander; Telcs, Andras
2001
Manifolds and graphs with slow heat kernel decay. Zbl 1003.58025
Barlow, Martin; Coulhon, Thierry; Grigor&rsquo;yan, Alexander
2001
A geometric approach to on-diagonal heat kernel lower bounds on groups. Zbl 1137.58307
Coulhon, Thierry; Grigor&rsquo;yan, Alexander; Pittet, Christophe
2001
Heat kernels on manifolds, graphs and fractals. Zbl 1057.58010
Grigor&rsquo;yan, Alexander
2001
XIIIth international congress on mathematical physics. Proceedings of the ICMP 2000, Imperial College, London, Great Britain, July 17–22, 2000. Zbl 0994.00023
2001
Asymptotic separation for independent trajectories of Markov processes. Zbl 0973.58020
Grigor&rsquo;yan, Alexander; Kelbert, Mark
2001
Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs. Zbl 1001.58022
Chung, Fan; Grigor&rsquo;yan, Alexander; Yau, Shing-Tung
2000
On Hardy-Littlewood inequality for Brownian motion on Riemannian manifolds. Zbl 1026.58028
Grigor&rsquo;yan, Alexander; Kelbert, Mark
2000
Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds. Zbl 0927.58019
Grigor&rsquo;yan, Alexander
1999
Estimates of heat kernels on Riemannian manifolds. Zbl 0985.58007
Grigor&rsquo;yan, Alexander
1999
Escape rate of Brownian motion on Riemannian manifolds. Zbl 1020.58024
Grigor&rsquo;yan, Alexander
1999
Isoperimetric inequalities and capacities on Riemannian manifolds. Zbl 0947.58034
Grigor&rsquo;yan, Alexander
1999
Heat kernel on connected sums of Riemannian manifolds. Zbl 0957.58023
Grigor&rsquo;yan, Alexander; Saloff-Coste, Laurent
1999
Decomposition of a metric space by capacitors. Zbl 0976.31006
Grigor&rsquo;yan, A.; Yau, S.-T.
1999
Random walks on graphs with regular volume growth. Zbl 0918.60053
Coulhon, T.; Grigoryan, A.
1998
A Liouville property for Schrödinger operators. Zbl 0938.31007
Grigor&rsquo;yan, Alexander; Hansen, Wolfhard
1998
The heat kernel of hyperbolic space. Zbl 0921.58063
Grigor&rsquo;yan, Alexander; Noguchi, Masakazu
1998
Range of fluctuation of Brownian motion on a complete Riemannian manifold. Zbl 0934.58023
Grigor&rsquo;yan, Alexander; Kelbert, Mark
1998
Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds. Zbl 0865.58042
Grigor&rsquo;yan, Alexander
1997
On-diagonal lower bounds for heat kernels and Markov chains. Zbl 0920.58064
Coulhon, Thierry; Grigor&rsquo;yan, Alexander
1997
Eigenvalues and diameters for manifolds and graphs. Zbl 0890.58093
Chung, F. R. K.; Grigor&rsquo;yan, A.; Yau, S.-T.
1997
Upper bounds for eigenvalues of the discrete and continuous Laplace operators. Zbl 0844.53029
Chung, F. R. K.; Grigor&rsquo;yan, A.; Yau, Shing-Tung
1996
Heat kernels, volume growth and anti-isoperimetric inequalities. Zbl 0873.58062
Coulhon, Thierry; Grigor&rsquo;yan, Alexander
1996
Upper bounds of derivatives of the heat kernel on an arbitrary complete manifold. Zbl 0842.58070
Grigor&rsquo;yan, Alexander
1995
Heat kernel of a noncompact Riemannian manifold. Zbl 0829.58041
Grigor&rsquo;yan, Alexander
1995
Heat kernel upper bounds on a complete non-compact manifold. Zbl 0810.58040
Grigor&rsquo;yan, Alexander
1994
Integral maximum principle and its applications. Zbl 0812.58082
Grigor&rsquo;yan, Alexander
1994
...and 21 more Documents
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### 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
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### 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. Serie Quarta 10 Duke Mathematical Journal 9 Communications in Mathematical Physics 9 Journal of Mathematical Physics 9 Mathematical Notes 9 Journal of the Mathematical Society of Japan 9 Communications in Partial Differential Equations 8 Journal d’Analyse Mathématique 8 Manuscripta Mathematica 8 Science China. Mathematics 7 Mathematische Nachrichten 7 Memoirs of the American Mathematical Society 7 Results in Mathematics 7 NoDEA. Nonlinear Differential Equations and Applications 7 The Journal of Fourier Analysis and Applications 7 Communications in Contemporary Mathematics 7 Journal of the Australian Mathematical Society 6 Geometriae Dedicata 5 Applicable Analysis 5 Archive for Rational Mechanics and Analysis 5 Communications on Pure and Applied Mathematics 5 Israel Journal of Mathematics 5 Archiv der Mathematik 5 Inventiones Mathematicae 5 Pacific Journal of Mathematics 5 Tohoku Mathematical Journal. Second Series 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Applied and Computational Harmonic Analysis 5 Journal of Mathematical Sciences (New York) 5 Bulletin des Sciences Mathématiques 5 Journal of the European Mathematical Society (JEMS) 5 Communications on Pure and Applied Analysis 5 Frontiers of Mathematics in China 5 Journal of Spectral Theory 4 Journal of Statistical Physics 4 Arkiv för Matematik 4 Proceedings of the London Mathematical Society. Third Series 4 Chinese Annals of Mathematics. Series B 4 Applied Mathematics Letters 4 Acta Mathematica Sinica. 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
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### 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)