Edit Profile (opens in new tab) Knopf, Dan Co-Author Distance Author ID: knopf.dan Published as: Knopf, Dan Documents Indexed: 38 Publications since 2000, including 6 Books and 2 Additional arXiv Preprints Co-Authors: 26 Co-Authors with 32 Joint Publications 537 Co-Co-Authors all top 5 Co-Authors 6 single-authored 14 Isenberg, James A. 8 Chow, Bennett 6 Angenent, Sigurd Bernardus 6 Guenther, Christine M. 6 Lu, Peng 5 Ni, Lei 4 Chu, Sunchin 4 Glickenstein, David 4 Ivey, Thomas A. 4 Luo, Feng 4 Šešum, Nataša 3 Gang, Zhou 3 Garfinkle, David 3 Wu, Haotian 2 Ilmanen, Thomas 2 Young, Andrea 1 Caputo, M. Cristina 1 Carson, Timothy 1 Deblois, Jason 1 Ecker, Klaus 1 Farrell, F. Thomas 1 Feldman, Mikhail 1 McLeod, Kevin 1 Ontaneda, Pedro 1 Sigal, Israel Michael 1 Topping, Peter Miles all top 5 Serials 5 Communications in Analysis and Geometry 5 Mathematical Surveys and Monographs 3 Journal für die Reine und Angewandte Mathematik 2 Nonlinearity 2 Journal of Differential Geometry 2 Proceedings of the American Mathematical Society 2 The Journal of Geometric Analysis 2 Mathematical Research Letters 1 Advances in Mathematics 1 Duke Mathematical Journal 1 Memoirs of the American Mathematical Society 1 Transactions of the American Mathematical Society 1 IMRN. International Mathematics Research Notices 1 Geometric and Functional Analysis. GAFA 1 Communications in Partial Differential Equations 1 Communications in Contemporary Mathematics 1 Algebraic & Geometric Topology 1 Pure and Applied Mathematics Quarterly Fields 36 Differential geometry (53-XX) 18 Global analysis, analysis on manifolds (58-XX) 15 Partial differential equations (35-XX) 6 Manifolds and cell complexes (57-XX) 2 Numerical analysis (65-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 31 Publications have been cited 978 times in 702 Documents Cited by ▼ Year ▼ The Ricci flow: an introduction. Zbl 1086.53085 Chow, Bennett; Knopf, Dan 261 2004 The Ricci flow: techniques and applications. Part I: Geometric aspects. Zbl 1157.53034 Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei 197 2007 Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons. Zbl 1069.53036 Feldman, Mikhail; Ilmanen, Tom; Knopf, Dan 101 2003 The Ricci flow: techniques and applications. Part II: Analytic aspects. Zbl 1157.53035 Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei 73 2008 The Ricci flow: techniques and applications. Part III: Geometric-analytic aspects. Zbl 1216.53057 Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei 64 2010 Stability of the Ricci flow at Ricci-flat metrics. Zbl 1028.53043 Guenther, Christine; Isenberg, James; Knopf, Dan 32 2002 An example of neckpinching for Ricci flow on \(S^{n+1}\). Zbl 1064.58022 Angenent, Sigurd; Knopf, Dan 31 2004 Precise asymptotics of the Ricci flow neckpinch. Zbl 1145.53049 Angenent, Sigurd B.; Knopf, Dan 22 2007 Universality in mean curvature flow neckpinches. Zbl 1329.53093 Gang, Zhou; Knopf, Dan 17 2015 Quasi-convergence of model geometries under the Ricci flow. Zbl 1020.53044 Knopf, Dan; McLeod, Kevin 16 2001 Degenerate neckpinches in Ricci flow. Zbl 1329.53102 Angenent, Sigurd B.; Isenberg, James; Knopf, Dan 16 2015 Local monotonicity and mean value formulas for evolving Riemannian manifolds. Zbl 1170.35050 Ecker, Klaus; Knopf, Dan; Ni, Lei; Topping, Peter 14 2008 The Ricci flow: techniques and applications. Part IV: Long-time solutions and related topics. Zbl 1341.53001 Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei 14 2015 A lower bound for the diameter of solutions to the Ricci flow with nonzero \(H^1(M^n, \mathbb R)\). Zbl 1048.58022 Ilmanen, Tom; Knopf, Dan 12 2003 Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow. Zbl 1440.53106 Gang, Zhou; Knopf, Dan; Sigal, Israel Michael 12 2018 Estimating the trace-free Ricci tensor in Ricci flow. Zbl 1172.53043 Knopf, Dan 10 2009 Formal matched asymptotics for degenerate Ricci flow neckpinches. Zbl 1225.53061 Angenent, Sigurd B.; Isenberg, James; Knopf, Dan 10 2011 New Li-Yau-Hamilton inequalities for the Ricci flow via the space-time approach. Zbl 1048.53026 Chow, Bennett; Knopf, Dan 9 2002 Asymptotic stability of the cross curvature flow at a hyperbolic metric. Zbl 1168.53034 Knopf, Dan; Young, Andrea 7 2009 Ricci flow neckpinches without rotational symmetry. Zbl 1357.53078 Isenberg, James; Knopf, Dan; Šešum, Nataša 7 2016 Quasi-convergence of the Ricci flow. Zbl 1027.53075 Knopf, Dan 6 2000 Positivity of Ricci curvature under the Kähler-Ricci flow. Zbl 1118.53045 Knopf, Dan 6 2006 Non-Kähler Ricci flow singularities modeled on Kähler-Ricci solitons. Zbl 1431.53103 Isenberg, James; Knopf, Dan; Šešum, Nataša 6 2019 Minimally invasive surgery for Ricci flow singularities. Zbl 1258.53066 Angenent, Sigurd B.; Caputo, M. Cristina; Knopf, Dan 6 2012 Convergence and stability of locally \(\mathbb R^N\)-invariant solutions of Ricci flow. Zbl 1176.53068 Knopf, Dan 6 2009 Dynamic instability of \(\mathbb {CP}^N\) under Ricci flow. Zbl 1408.53090 Knopf, Dan; Šešum, Nataša 5 2019 Linear stability of homogeneous Ricci solutions. Zbl 1126.53040 Guenther, Christine; Isenberg, James; Knopf, Dan 5 2006 Ricci solitons, conical singularities, and nonuniqueness. Zbl 1503.53091 Angenent, Sigurd B.; Knopf, Dan 4 2022 Cross curvature flow on a negatively curved solid torus. Zbl 1211.53083 DeBlois, Jason; Knopf, Dan; Young, Andrea 4 2010 Sphere bundles with \(1/4\)-pinched fiberwise metrics. Zbl 1369.57032 Farrell, Thomas; Gang, Zhou; Knopf, Dan; Ontaneda, Pedro 3 2017 Hamilton’s injectivity radius estimate for sequences with almost nonnegative curvature operators. Zbl 1041.53042 Chow, Bennett; Knopf, Dan; Lu, Peng 2 2002 Ricci solitons, conical singularities, and nonuniqueness. Zbl 1503.53091 Angenent, Sigurd B.; Knopf, Dan 4 2022 Non-Kähler Ricci flow singularities modeled on Kähler-Ricci solitons. Zbl 1431.53103 Isenberg, James; Knopf, Dan; Šešum, Nataša 6 2019 Dynamic instability of \(\mathbb {CP}^N\) under Ricci flow. Zbl 1408.53090 Knopf, Dan; Šešum, Nataša 5 2019 Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow. Zbl 1440.53106 Gang, Zhou; Knopf, Dan; Sigal, Israel Michael 12 2018 Sphere bundles with \(1/4\)-pinched fiberwise metrics. Zbl 1369.57032 Farrell, Thomas; Gang, Zhou; Knopf, Dan; Ontaneda, Pedro 3 2017 Ricci flow neckpinches without rotational symmetry. Zbl 1357.53078 Isenberg, James; Knopf, Dan; Šešum, Nataša 7 2016 Universality in mean curvature flow neckpinches. Zbl 1329.53093 Gang, Zhou; Knopf, Dan 17 2015 Degenerate neckpinches in Ricci flow. Zbl 1329.53102 Angenent, Sigurd B.; Isenberg, James; Knopf, Dan 16 2015 The Ricci flow: techniques and applications. Part IV: Long-time solutions and related topics. Zbl 1341.53001 Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei 14 2015 Minimally invasive surgery for Ricci flow singularities. Zbl 1258.53066 Angenent, Sigurd B.; Caputo, M. Cristina; Knopf, Dan 6 2012 Formal matched asymptotics for degenerate Ricci flow neckpinches. Zbl 1225.53061 Angenent, Sigurd B.; Isenberg, James; Knopf, Dan 10 2011 The Ricci flow: techniques and applications. Part III: Geometric-analytic aspects. Zbl 1216.53057 Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei 64 2010 Cross curvature flow on a negatively curved solid torus. Zbl 1211.53083 DeBlois, Jason; Knopf, Dan; Young, Andrea 4 2010 Estimating the trace-free Ricci tensor in Ricci flow. Zbl 1172.53043 Knopf, Dan 10 2009 Asymptotic stability of the cross curvature flow at a hyperbolic metric. Zbl 1168.53034 Knopf, Dan; Young, Andrea 7 2009 Convergence and stability of locally \(\mathbb R^N\)-invariant solutions of Ricci flow. Zbl 1176.53068 Knopf, Dan 6 2009 The Ricci flow: techniques and applications. Part II: Analytic aspects. Zbl 1157.53035 Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei 73 2008 Local monotonicity and mean value formulas for evolving Riemannian manifolds. Zbl 1170.35050 Ecker, Klaus; Knopf, Dan; Ni, Lei; Topping, Peter 14 2008 The Ricci flow: techniques and applications. Part I: Geometric aspects. Zbl 1157.53034 Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei 197 2007 Precise asymptotics of the Ricci flow neckpinch. Zbl 1145.53049 Angenent, Sigurd B.; Knopf, Dan 22 2007 Positivity of Ricci curvature under the Kähler-Ricci flow. Zbl 1118.53045 Knopf, Dan 6 2006 Linear stability of homogeneous Ricci solutions. Zbl 1126.53040 Guenther, Christine; Isenberg, James; Knopf, Dan 5 2006 The Ricci flow: an introduction. Zbl 1086.53085 Chow, Bennett; Knopf, Dan 261 2004 An example of neckpinching for Ricci flow on \(S^{n+1}\). Zbl 1064.58022 Angenent, Sigurd; Knopf, Dan 31 2004 Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons. Zbl 1069.53036 Feldman, Mikhail; Ilmanen, Tom; Knopf, Dan 101 2003 A lower bound for the diameter of solutions to the Ricci flow with nonzero \(H^1(M^n, \mathbb R)\). Zbl 1048.58022 Ilmanen, Tom; Knopf, Dan 12 2003 Stability of the Ricci flow at Ricci-flat metrics. Zbl 1028.53043 Guenther, Christine; Isenberg, James; Knopf, Dan 32 2002 New Li-Yau-Hamilton inequalities for the Ricci flow via the space-time approach. Zbl 1048.53026 Chow, Bennett; Knopf, Dan 9 2002 Hamilton’s injectivity radius estimate for sequences with almost nonnegative curvature operators. Zbl 1041.53042 Chow, Bennett; Knopf, Dan; Lu, Peng 2 2002 Quasi-convergence of model geometries under the Ricci flow. Zbl 1020.53044 Knopf, Dan; McLeod, Kevin 16 2001 Quasi-convergence of the Ricci flow. Zbl 1027.53075 Knopf, Dan 6 2000 all cited Publications top 5 cited Publications all top 5 Cited by 668 Authors 14 Ma, Li 12 Isenberg, James A. 12 Knopf, Dan 11 Azami, Shahroud 11 Cao, Huai-Dong 11 Wu, Jiayong 10 García-Río, Eduardo 10 Lu, Peng 9 Cao, Xiaodong 9 Lee, Man-Chun 9 Zhang, Yongjia 8 Abolarinwa, Abimbola 8 Chow, Bennett 8 Deruelle, Alix 8 Sharma, Ramesh 8 Topping, Peter Miles 7 Bamler, Richard H. 7 Ghosh, Amalendu 7 Mantegazza, Carlo 7 Streets, Jeffrey D. 7 Suh, Young Jin 7 Wang, Linfeng 7 Zhang, Qi-Shuhuason 7 Zhu, Anqiang 6 Baltazar, Halyson I. 6 Chan, Pak-Yeung 6 Cheng, Liang 6 Cho, Jong Taek 6 De, Uday Chand 6 Gang, Zhou 6 Guenther, Christine M. 6 Guo, Hongxin 6 Haslhofer, Robert 6 Šešum, Nataša 6 Wu, Guoqiang 6 Wu, Haotian 6 Zhang, Zhou 5 Cabezas-Rivas, Esther 5 Carfora, Mauro 5 Catino, Giovanni 5 Colding, Tobias Holck 5 Collins, Tristan Clifford 5 Fernández-López, Manuel 5 Kröncke, Klaus 5 Lott, John 5 Lüst, Dieter 5 Ma, Zilu 5 Minicozzi, William Philip II 5 Munteanu, Ovidiu 5 Stepanov, Sergeĭ Evgen’evich 5 Tam, Luen-Fai 5 Tian, Gang 5 Tosatti, Valentino 5 Wylie, William C. 5 Yan, Zaili 4 Buzano, Reto 4 Chen, Chih-Wei 4 Chen, Xiuxiong 4 De Biasio, Davide 4 Gianniotis, Panagiotis 4 Gomes, José Nazareno Vieira 4 Hou, Songbo 4 Kotschwar, Brett L. 4 Lakzian, Sajjad 4 Li, Yu 4 Loi, Andrea 4 Philipowski, Robert 4 Pulemotov, Artem 4 Razavi, Asadollah 4 Simon, Miles 4 Wang, Jianhong 4 Wang, Jiaping 4 Xu, Guoyi 4 Yang, Bo 4 Yildiz, Ahmet 4 Zhang, Zhenlei 3 Bahuaud, Eric 3 Batista, Rondinelle Marcolino 3 Bidabad, Behroz 3 Brendle, Simon 3 Conlon, Ronan J. 3 Coulibaly-Pasquier, Koléhè Abdoulaye 3 Di Giovanni, Francesco 3 Giesen, Gregor 3 Glickenstein, David 3 Hall, Stuart James 3 He, Fei 3 Hsu, Shu-Yu 3 Kimura, Makoto 3 Kleiner, Bruce 3 Kunikawa, Keita 3 Lafuente, Ramiro A. 3 Lasso Andino, Óscar 3 Lauret, Jorge 3 Li, Haozhao 3 Li, Xiang-Dong 3 Li, Yi 3 Mandal, Krishanu 3 Mazzieri, Lorenzo 3 Naik, Devaraja Mallesha ...and 568 more Authors all top 5 Cited in 186 Serials 67 The Journal of Geometric Analysis 36 Proceedings of the American Mathematical Society 29 Calculus of Variations and Partial Differential Equations 21 Transactions of the American Mathematical Society 20 Advances in Mathematics 20 Journal of Functional Analysis 20 Mathematische Annalen 18 Annals of Global Analysis and Geometry 16 Journal of Geometry and Physics 15 Journal für die Reine und Angewandte Mathematik 15 Geometry & Topology 12 Geometriae Dedicata 12 Mathematische Zeitschrift 12 Differential Geometry and its Applications 10 Journal of Mathematical Physics 9 Journal of Mathematical Analysis and Applications 9 Geometric and Functional Analysis. GAFA 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Journal of Geometry 7 Manuscripta Mathematica 7 Results in Mathematics 7 International Journal of Geometric Methods in Modern Physics 6 Inventiones Mathematicae 6 Journal of the Korean Mathematical Society 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Chinese Annals of Mathematics. Series B 6 Communications in Partial Differential Equations 6 Journal of High Energy Physics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Journal of Differential Geometry 5 Pacific Journal of Mathematics 5 Science China. Mathematics 4 Communications in Mathematical Physics 4 Communications on Pure and Applied Mathematics 4 Mathematical Notes 4 Duke Mathematical Journal 4 Mathematische Nachrichten 4 Mediterranean Journal of Mathematics 3 Classical and Quantum Gravity 3 Letters in Mathematical Physics 3 Ukrainian Mathematical Journal 3 Annales de l’Institut Fourier 3 Journal of the London Mathematical Society. Second Series 3 Memoirs of the American Mathematical Society 3 Monatshefte für Mathematik 3 Osaka Journal of Mathematics 3 Tôhoku Mathematical Journal. Second Series 3 Bulletin of the Iranian Mathematical Society 3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 3 International Journal of Mathematics 3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 3 Potential Analysis 3 Journal of the European Mathematical Society (JEMS) 3 Communications of the Korean Mathematical Society 3 DGDS. Differential Geometry – Dynamical Systems 3 Advances in Geometry 3 Journal of Evolution Equations 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Journal of Fixed Point Theory and Applications 3 Frontiers of Mathematics in China 3 European Journal of Mathematics 2 Indian Journal of Pure & Applied Mathematics 2 Journal of Computational Physics 2 Nuclear Physics. B 2 Reports on Mathematical Physics 2 Beiträge zur Algebra und Geometrie 2 Fortschritte der Physik 2 Acta Mathematica 2 Kyungpook Mathematical Journal 2 Siberian Mathematical Journal 2 Bulletin of the Korean Mathematical Society 2 Note di Matematica 2 Journal of the American Mathematical Society 2 Annals of Physics 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Stochastic Processes and their Applications 2 Bulletin of the American Mathematical Society. New Series 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Russian Mathematics 2 International Journal of Modern Physics D 2 Turkish Journal of Mathematics 2 Annales Academiae Scientiarum Fennicae. Mathematica 2 Annals of Mathematics. Second Series 2 Acta Mathematica Sinica. English Series 2 Communications in Contemporary Mathematics 2 Acta Mathematica Scientia. Series B. (English Edition) 2 JP Journal of Geometry and Topology 2 Boletim da Sociedade Paranaense de Matemática. Terceira Série 2 Journal of Mathematical Physics, Analysis, Geometry 2 International Electronic Journal of Geometry 2 Analysis and Mathematical Physics 2 Afrika Matematika 2 Axioms 2 Analysis and Geometry in Metric Spaces 2 Complex Manifolds 2 Transactions of the American Mathematical Society. Series B 1 International Journal of Modern Physics A 1 Analysis Mathematica 1 Archive for Rational Mechanics and Analysis 1 Bulletin of the Australian Mathematical Society ...and 86 more Serials all top 5 Cited in 40 Fields 638 Differential geometry (53-XX) 166 Partial differential equations (35-XX) 160 Global analysis, analysis on manifolds (58-XX) 47 Several complex variables and analytic spaces (32-XX) 30 Relativity and gravitational theory (83-XX) 27 Quantum theory (81-XX) 26 Manifolds and cell complexes (57-XX) 17 Algebraic geometry (14-XX) 11 Dynamical systems and ergodic theory (37-XX) 11 Probability theory and stochastic processes (60-XX) 10 Topological groups, Lie groups (22-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 6 Functions of a complex variable (30-XX) 6 Functional analysis (46-XX) 6 Numerical analysis (65-XX) 6 Fluid mechanics (76-XX) 4 Operator theory (47-XX) 4 Mechanics of particles and systems (70-XX) 3 Real functions (26-XX) 3 Geometry (51-XX) 3 Convex and discrete geometry (52-XX) 3 Computer science (68-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Measure and integration (28-XX) 2 Potential theory (31-XX) 2 Ordinary differential equations (34-XX) 2 Astronomy and astrophysics (85-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 General topology (54-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year