Edit Profile (opens in new tab) Grigor’yan, Alexander Asaturovich Co-Author Distance 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: 160 Publications since 1979, including 2 Books and 6 Additional arXiv Preprints 6 Contributions as Editor Co-Authors: 93 Co-Authors with 119 Joint Publications 3,973 Co-Co-Authors all top 5 Co-Authors 47 single-authored 21 Yau, Shing-Tung 18 Hu, Jiaxin 13 Muranov, Yuriĭ Vladimirovich 11 Lin, Yong 9 Bendikov, Alexander D. 9 Coulhon, Thierry 9 Saloff-Coste, Laurent 8 Lau, Kasing 7 Hu, Eryan 6 Molchanov, Stanislav Alekseevich 4 Ishiwata, Satoshi 4 Jiménez Benitez, Rolando 4 Kelbert, Mark Ya. 4 Nadirashvili, Nikolai S. 4 Sun, Yuhua 3 Barlow, Martin T. 3 Cao, Jun 3 Chung, Fan 3 Kumagai, Takashi 3 Pittet, Christophe 3 Telcs, András 3 Verbitsky, Igor E. 3 Yang, Yunyan 2 Fokas, Athanassios S. 2 Hansen, Wolfhard 2 Huang, Xueping 2 Kibble, Tom W. B. 2 Liu, Liguang 2 Masamune, Jun 2 Yang, Meng 2 Zegarlinski, Boguslaw 1 Auscher, Pascal 1 Avkhadiev, Farit Gabidinovich 1 Barabasheva, Yu. M. 1 Botvinnik, V. A. 1 Chirka, Evgeniĭ Mikhaĭlovich 1 Devyatkova, G. N. 1 Drinfeld, Vladimir Gershonovich 1 Dubinin, Vladimir N. 1 Falconer, Kenneth J. 1 Fan, Ai Hua 1 Faraji, Shokoufe 1 Feng, De-Jun 1 Gilkey, Peter B. 1 Gol’dstein, Vladimir Mikailovitch 1 Goryainov, Viktor V. 1 Hsu, Elton P. 1 Il’yashenko, Yuliĭ Sergeevich 1 Jakobson, Dmitry 1 Jørgensen, Palle E. T. 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, Aleksandr Vasil’evich 1 Martio, Olli 1 Netrusov, Yuri 1 Noguchi, Masakazu 1 Ouyang, Shunxiang 1 Papageorgiou, Effie G. 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 Sürig, Philipp 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 Zhang, Haohang 1 Zhang, Hongwei 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 Journal d’Analyse Mathématique 3 Annales de l’Institut Fourier 3 The Annals of Probability 3 Mathematische Annalen 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Mathematics of the USSR, Sbornik 3 The Asian Journal of Mathematics 2 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 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 Proceedings of the London Mathematical Society. Third Series 2 Soviet Mathematics. Doklady 2 Soviet Mathematics 2 Revista Matemática Iberoamericana 2 Forum Mathematicum 2 Potential Analysis 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 2 Pure and Applied Mathematics Quarterly 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 Pacific Journal of Mathematics 1 Tôhoku Mathematical Journal. Second Series 1 Voprosy Istorii Estestvoznaniya i Tekhniki 1 Topology and its Applications 1 Probability Theory and Related Fields 1 The Journal of Geometric Analysis 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 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 Trudy Tbilisskogo Universiteta. Matematika, Mekhanika, Astronomiya 1 Rendiconti del Seminario Matematico. Universitá e Politecnico di Torino 1 Contemporary Mathematics 1 Proceedings of the Steklov Institute of 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 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 1 Global and Stochastic Analysis 1 ICCM Notices 1 Journal of Fractal Geometry 1 Pure and Applied Functional Analysis 1 Advances in Analysis and Geometry all top 5 Fields 82 Global analysis, analysis on manifolds (58-XX) 69 Partial differential equations (35-XX) 51 Probability theory and stochastic processes (60-XX) 26 Potential theory (31-XX) 23 Measure and integration (28-XX) 20 Combinatorics (05-XX) 19 Operator theory (47-XX) 14 Differential geometry (53-XX) 13 Algebraic topology (55-XX) 10 Functional analysis (46-XX) 6 General and overarching topics; collections (00-XX) 6 History and biography (01-XX) 6 Category theory; homological algebra (18-XX) 5 Functions of a complex variable (30-XX) 5 Manifolds and cell complexes (57-XX) 4 Real functions (26-XX) 3 Ordinary differential equations (34-XX) 2 Number theory (11-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) 2 Quantum theory (81-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 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 139 Publications have been cited 3,891 times in 2,087 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 435 1999 Heat kernel and analysis on manifolds. Zbl 1206.58008 Grigor’yan, Alexander 394 2009 Heat kernels on weighted manifolds and applications. Zbl 1106.58016 Grigor’yan, Alexander 115 2006 Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds. Zbl 0865.58042 Grigor’yan, Alexander 89 1997 Yamabe type equations on graphs. Zbl 1351.35038 Grigor’yan, Alexander; Lin, Yong; Yang, Yunyan 87 2016 Heat kernel upper bounds on a complete non-compact manifold. Zbl 0810.58040 Grigor’yan, Alexander 86 1994 Kazdan-Warner equation on graph. Zbl 1366.58006 Grigor’yan, Alexander; Lin, Yong; Yang, Yunyan 81 2016 The heat equation on noncompact Riemannian manifolds. Zbl 0776.58035 Grigor’yan, A. A. 77 1992 Heat kernels on metric measure spaces and an application to semilinear elliptic equations. Zbl 1018.60075 Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 76 2003 Estimates of heat kernels on Riemannian manifolds. Zbl 0985.58007 Grigor’yan, Alexander 72 1999 Two-sided estimates of heat kernels on metric measure spaces. Zbl 1252.35148 Grigor’yan, Alexander; Telcs, Andras 71 2012 Heat kernels and function theory on metric measure spaces. Zbl 1048.58021 Grigor’yan, Alexander 67 2003 Heat kernel upper bounds for jump processes and the first exit time. Zbl 1158.60039 Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi 67 2009 Heat equation on noncompact Riemannian manifolds. Zbl 0743.58031 Grigor’yan, A. A. 64 1991 Stability results for Harnack inequalities. Zbl 1115.58024 Grigor’yan, Alexander; Saloff-Coste, Laurent 63 2005 Existence of positive solutions to some nonlinear equations on locally finite graphs. Zbl 1384.34035 Grigor’yan, Alexander; Lin, Yong; Yang, YunYan 63 2017 Random walks on graphs with regular volume growth. Zbl 0918.60053 Coulhon, T.; Grigoryan, A. 55 1998 The heat kernel of hyperbolic space. Zbl 0921.58063 Grigor’yan, Alexander; Noguchi, Masakazu 54 1998 Introduction to analysis on graphs. Zbl 1416.05002 Grigor’yan, Alexander 52 2018 On the equivalence of parabolic Harnack inequalities and heat kernel estimates. Zbl 1281.58016 Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi 51 2012 Sub-Gaussian estimates of heat kernels on infinite graphs. Zbl 1010.35016 Grigor’yan, Alexander; Telcs, Andras 48 2001 On stochastic completeness of jump processes. Zbl 1408.60076 Grigor’yan, Alexander; Huang, Xueping; Masamune, Jun 47 2012 On stochastically complete manifolds. Zbl 0632.58041 Grigor’yan, A. A. 45 1987 Harnack inequalities and sub-Gaussian estimates for random walks. Zbl 1011.60021 Grigor’yan, A.; Telcs, A. 44 2002 Eigenvalues of elliptic operators and geometric applications. Zbl 1061.58027 Grigor’yan, Alexander; Netrusov, Yuri; Yau, Shing-Tung 44 2004 On-diagonal lower bounds for heat kernels and Markov chains. Zbl 0920.58064 Coulhon, Thierry; Grigor’yan, Alexander 43 1997 On nonnegative solutions of the inequality \(\Delta u+u^{\sigma }\leq 0\) on Riemannian manifolds. Zbl 1296.58011 Grigor’yan, Alexander; Sun, Yuhua 43 2014 Dirichlet heat kernel in the exterior of a compact set. Zbl 1037.58018 Grigor’yan, Alexander; Saloff-Coste, Laurent 41 2002 Upper bounds of derivatives of the heat kernel on an arbitrary complete manifold. Zbl 0842.58070 Grigor’yan, Alexander 41 1995 Upper bounds of heat kernels on doubling spaces. Zbl 1524.47050 Grigor’yan, Alexander; Hu, Jiaxin 39 2014 Heat kernel on manifolds with ends. Zbl 1239.58016 Grigor’yan, Alexander; Saloff-Coste, Laurent 38 2009 Manifolds and graphs with slow heat kernel decay. Zbl 1003.58025 Barlow, Martin; Coulhon, Thierry; Grigor’yan, Alexander 37 2001 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 35 2015 Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces. Zbl 1154.47034 Grigor’yan, Alexander; Hu, Jiaxin 33 2008 Homotopy theory for digraphs. Zbl 1312.05063 Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung 33 2014 Isotropic Markov semigroups on ultra-metric spaces. Zbl 1322.60151 Bendikov, A. D.; Grigor’yan, A. A.; Pittet, Ch; Woess, W. 32 2014 Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs. Zbl 1001.58022 Chung, Fan; Grigor’yan, Alexander; Yau, Shing-Tung 31 2000 Hitting probabilities for Brownian motion on Riemannian manifolds. Zbl 1042.58022 Grigor’yan, Alexander; Saloff-Coste, Laurent 30 2002 Isoperimetric inequalities and capacities on Riemannian manifolds. Zbl 0947.58034 Grigor’yan, Alexander 30 1999 Estimates of heat kernels for non-local regular Dirichlet forms. Zbl 1304.47058 Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 30 2014 On the existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds. Zbl 0612.31007 Grigor’yan, A. A. 29 1987 Heat kernels and Green functions on metric measure spaces. Zbl 1293.35128 Grigor’yan, Alexander; Hu, Jiaxin 29 2014 Parabolicity and stochastic completeness of manifolds in terms of the Green formula. Zbl 1356.58007 Grigor’yan, Alexander; Masamune, Jun 27 2013 A geometric approach to on-diagonal heat kernel lower bounds on groups. Zbl 1137.58307 Coulhon, Thierry; Grigor’yan, Alexander; Pittet, Christophe 26 2001 Upper bounds for eigenvalues of the discrete and continuous Laplace operators. Zbl 0844.53029 Chung, F. R. K.; Grigor’yan, A.; Yau, Shing-Tung 26 1996 Escape rate of Brownian motion on Riemannian manifolds. Zbl 1020.58024 Grigor’yan, Alexander 25 1999 Two-sided estimates of heat kernels of jump type Dirichlet forms. Zbl 1468.35081 Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 25 2018 The discrete integral maximum principle and its applications. Zbl 1096.60023 Coulhon, Thierry; Grigor’yan, Alexander; Zucca, Fabio 24 2005 Cohomology of digraphs and (undirected) graphs. Zbl 1329.05132 Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung 23 2015 Existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds. Zbl 0596.31004 Grigor’yan, A. A. 23 1985 Integral maximum principle and its applications. Zbl 0812.58082 Grigor’yan, Alexander 22 1994 A Liouville property for Schrödinger operators. Zbl 0938.31007 Grigor’yan, Alexander; Hansen, Wolfhard 22 1998 Heat kernels on metric spaces with doubling measure. Zbl 1197.35129 Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 21 2009 Heat kernel and Lipschitz-Besov spaces. Zbl 1327.35130 Grigor’yan, Alexander; Liu, Liguang 20 2015 On the existence of positive solutions of semilinear elliptic inequalities on Riemannian manifolds. Zbl 1185.35344 Grigor’yan, Alexander; Kondratiev, Vladimir A. 20 2010 Comparison inequalities for heat semigroups and heat kernels on metric measure spaces. Zbl 1207.58021 Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 19 2010 Heat kernels on metric measure spaces with regular volume growth. Zbl 1217.58018 Grigor’yan, Alexander 19 2010 On the dichotomy in the heat kernel two sided estimates. Zbl 1162.47037 Grigor’yan, Alexander; Kumagai, Takashi 18 2008 Surgery of the Faber-Krahn inequality and applications to heat kernel bounds. Zbl 1334.58019 Grigor’yan, Alexander; Saloff-Coste, Laurent 18 2016 Stochastically complete manifolds and summable harmonic functions. Zbl 0677.60086 Grigor’yan, A. A. 18 1989 Path complexes and their homologies. Zbl 1448.05171 Grigor’yan, A. A.; Lin, Yong; Muranov, Yu. V.; Yau, Shing-Tung 18 2020 On the path homology theory of digraphs and Eilenberg-Steenrod axioms. Zbl 1391.05125 Grigor’yan, Alexander; Jimenez, Rolando; Muranov, Yuri; Yau, Shing-Tung 18 2018 Heat kernels on metric measure spaces. Zbl 1323.58018 Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 16 2014 Graphs associated with simplicial complexes. Zbl 1297.05269 Grigor’yan, A.; Muranov, Yu. V.; Yau, Shing-Tung 16 2014 Negative eigenvalues of two-dimensional Schrödinger operators. Zbl 1319.35128 Grigor’yan, Alexander; Nadirashvili, Nikolai 15 2015 Homologies of digraphs and Künneth formulas. Zbl 1381.05062 Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung 15 2017 Eigenvalues and diameters for manifolds and graphs. Zbl 0890.58093 Chung, F. R. K.; Grigor’yan, A.; Yau, S.-T. 14 1997 On isoperimetric profiles of product spaces. Zbl 1085.53027 Coulhon, Thierry; Grigor’yan, Alexander; Levin, Daniel 14 2003 On the existence of a Green’s function on a manifold. Zbl 0542.35025 Grigor’yan, A. A. 13 1983 Range of fluctuation of Brownian motion on a complete Riemannian manifold. Zbl 0934.58023 Grigor’yan, Alexander; Kelbert, Mark 13 1998 Heat kernel on connected sums of Riemannian manifolds. Zbl 0957.58023 Grigor’yan, Alexander; Saloff-Coste, Laurent 13 1999 On a class of Markov semigroups on discrete ultra-metric spaces. Zbl 1260.60142 Bendikov, Alexander; Grigor’yan, Alexander; Pittet, Christophe 13 2012 Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces. Zbl 1372.35123 Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 13 2017 Heat kernels on manifolds, graphs and fractals. Zbl 1057.58010 Grigor’yan, Alexander 12 2001 Volume growth and escape rate of Brownian motion on a Cartan-Hadamard manifold. Zbl 1167.58019 Grigor’yan, Alexander; Hsu, Elton 12 2009 Stochastically complete manifolds and summable harmonic functions. Zbl 0661.60090 Grigoryan, A. A. 12 1988 Isoperimetric properties of higher eigenvalues of elliptic operators. Zbl 1042.58017 Grigor’yan, Alexander; Yau, Shing-Tung 12 2003 Lower estimates for a perturbed Green function. Zbl 1158.35022 Grigor’yan, Alexander; Hansen, Wolfhard 11 2008 Path homology theory of multigraphs and quivers. Zbl 1404.55010 Grigor’yan, Alexander; Muranov, Yuri; Vershinin, Vladimir; Yau, Shing-Tung 11 2018 Pointwise estimates of solutions to nonlinear equations for nonlocal operators. Zbl 1475.35155 Grigor’yan, Alexander; Verbitsky, Igor 11 2020 Heat kernel on a manifold with a local Harnack inequality. Zbl 0845.58056 Grigor’yan, Alexander 10 1994 Decomposition of a metric space by capacitors. Zbl 0976.31006 Grigor’yan, A.; Yau, S.-T. 10 1999 Local and non-local Dirichlet forms on the Sierpiński carpet. Zbl 1426.28018 Grigor’yan, Alexander; Yang, Meng 10 2019 Dimension of spaces of harmonic functions. Zbl 0721.31003 Grigor’yan, A. A. 10 1990 On a cohomology of digraphs and Hochschild cohomology. Zbl 1353.05056 Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung 10 2016 Bounded solutions of the Schrödinger equation on noncompact Riemannian manifolds. Zbl 0744.58070 Grigor’yan, A. A. 9 1989 Pointwise estimates for transition probabilities of random walks on infinite graphs. Zbl 1048.60081 Coulhon, Thierry; Grigor’yan, Alexander 8 2003 On Liouville theorems for harmonic functions with finite Dirichlet integral. Zbl 0646.31009 Grigor’yan, A. A. 8 1987 Liouville theorems and external boundary value problems. Zbl 0639.58029 Grigor’yan, A. A.; Nadirashvili, N. S. 8 1987 On Hardy-Littlewood inequality for Brownian motion on Riemannian manifolds. Zbl 1026.58028 Grigor’yan, Alexander; Kelbert, Mark 8 2000 Heat kernel of a noncompact Riemannian manifold. Zbl 0829.58041 Grigor’yan, Alexander 8 1995 Heat kernel estimates on connected sums of parabolic manifolds. Zbl 1388.35078 Grigor’yan, Alexander; Ishiwata, Satoshi; Saloff-Coste, Laurent 8 2018 Gaussian upper bounds for the heat kernel and for its derivatives on a Riemannian manifold. Zbl 0885.58088 Grigor’yan, A. 7 1994 A lower bound for the number of negative eigenvalues of Schrödinger operators. Zbl 1356.53044 Grigor’yan, Alexander; Nadirashvili, Nikolai; Sire, Yannick 7 2016 Homology of path complexes and hypergraphs. Zbl 1422.05076 Grigor’yan, Alexander; Jimenez, Rolando; Muranov, Yuri; Yau, Shing-Tung 7 2019 Pointwise estimates for heat kernels of convolution-type operators. Zbl 06968912 Grigor’yan, Alexander; Kondratiev, Yuri; Piatnitski, Andrey; Zhizhina, Elena 7 2018 Heat kernels and Besov spaces on metric measure spaces. Zbl 1514.46027 Cao, Jun; Grigor’yan, Alexander 7 2022 Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula. Zbl 1387.60121 Grigor’yan, Alexander; Kajino, Naotaka 7 2017 Heat kernels and non-local Dirichlet forms on ultrametric spaces. Zbl 1469.35109 Bendikov, Alexander; Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 7 2021 Mathematical physics 2000. International congress, London, GB, 2000. Zbl 0949.00037 6 2000 On homology theories of cubical digraphs. Zbl 1527.55008 Grigor’yan, Alexander; Muranov, Yuri 1 2023 Asymptotic behavior of the heat Semigroup on certain Riemannian manifolds. Zbl 1532.58012 Grigor’yan, Alexander; Papageorgiou, Effie; Zhang, Hong-Wei 1 2023 Heat kernels and Besov spaces on metric measure spaces. Zbl 1514.46027 Cao, Jun; Grigor’yan, Alexander 7 2022 Analysis on fractal spaces and heat kernels. Zbl 1497.60104 Grigor’yan, Alexander 3 2022 Discrete tori and trigonometric sums. Zbl 1502.60117 Grigor’yan, Alexander; Lin, Yong; Yau, Shing-Tung 2 2022 Advances in path homology theory of digraphs. Zbl 1509.05081 Grigor’yan, Alexander 1 2022 Heat kernels and non-local Dirichlet forms on ultrametric spaces. Zbl 1469.35109 Bendikov, Alexander; Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 7 2021 Hardy’s inequality and Green function on metric measure spaces. Zbl 1462.31015 Cao, Jun; Grigor’yan, Alexander; Liu, Liguang 5 2021 Geometric analysis on manifolds with ends. Zbl 1476.58030 Grigor’yan, Alexander; Ishiwata, Satoshi; Saloff-Coste, Laurent 5 2021 Homology of digraphs. Zbl 1470.05042 Grigor’yan, A. A.; Muranov, Yu. V.; Jimenez, R. 4 2021 The pointwise existence and properties of heat kernel. Zbl 1476.35114 Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 2 2021 Analysis on manifolds and volume growth. Zbl 1476.58029 Grigor’yan, Alexander 2 2021 Hierarchical Schrödinger type operators: the case of locally bounded potentials. Zbl 1490.34105 Bendikov, Alexander; Grigor’yan, Alexander; Molchanov, Stanislav 1 2021 Path complexes and their homologies. Zbl 1448.05171 Grigor’yan, A. A.; Lin, Yong; Muranov, Yu. V.; Yau, Shing-Tung 18 2020 Pointwise estimates of solutions to nonlinear equations for nonlocal operators. Zbl 1475.35155 Grigor’yan, Alexander; Verbitsky, Igor 11 2020 Heat kernels and Besov spaces associated with second order divergence form elliptic operators. Zbl 1428.35148 Cao, Jun; Grigor’yan, Alexander 6 2020 Superlinear elliptic inequalities on manifolds. Zbl 1435.35169 Grigor’yan, Alexander; Sun, Yuhua; Verbitsky, Igor 6 2020 Local and non-local Dirichlet forms on the Sierpiński carpet. Zbl 1426.28018 Grigor’yan, Alexander; Yang, Meng 10 2019 Homology of path complexes and hypergraphs. Zbl 1422.05076 Grigor’yan, Alexander; Jimenez, Rolando; Muranov, Yuri; Yau, Shing-Tung 7 2019 On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds. Zbl 1430.58014 Grigor’yan, Alexander; Sun, Yuhua 5 2019 Pointwise estimates of solutions to semilinear elliptic equations and inequalities. Zbl 1421.35073 Grigor’yan, Alexander; Verbitsky, Igor 5 2019 Introduction to analysis on graphs. Zbl 1416.05002 Grigor’yan, Alexander 52 2018 Two-sided estimates of heat kernels of jump type Dirichlet forms. Zbl 1468.35081 Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 25 2018 On the path homology theory of digraphs and Eilenberg-Steenrod axioms. Zbl 1391.05125 Grigor’yan, Alexander; Jimenez, Rolando; Muranov, Yuri; Yau, Shing-Tung 18 2018 Path homology theory of multigraphs and quivers. Zbl 1404.55010 Grigor’yan, Alexander; Muranov, Yuri; Vershinin, Vladimir; Yau, Shing-Tung 11 2018 Heat kernel estimates on connected sums of parabolic manifolds. Zbl 1388.35078 Grigor’yan, Alexander; Ishiwata, Satoshi; Saloff-Coste, Laurent 8 2018 Pointwise estimates for heat kernels of convolution-type operators. Zbl 06968912 Grigor’yan, Alexander; Kondratiev, Yuri; Piatnitski, Andrey; Zhizhina, Elena 7 2018 Heat kernel estimates for an operator with a singular drift and isoperimetric inequalities. Zbl 1401.35145 Grigor’yan, Alexander; Ouyang, Shunxiang; Röckner, Michael 3 2018 Determination of the walk dimension of the Sierpiński gasket without using diffusion. Zbl 1416.28011 Grigor’yan, Alexander; Yang, Meng 3 2018 Fundamental groupoids of digraphs and graphs. Zbl 1458.05103 Grigor’yan, Alexander; Jimenez, Rolando; Muranov, Yuri 2 2018 Existence of positive solutions to some nonlinear equations on locally finite graphs. Zbl 1384.34035 Grigor’yan, Alexander; Lin, Yong; Yang, YunYan 63 2017 Homologies of digraphs and Künneth formulas. Zbl 1381.05062 Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung 15 2017 Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces. Zbl 1372.35123 Grigor’yan, Alexander; Hu, Eryan; Hu, Jiaxin 13 2017 Localized upper bounds of heat kernels for diffusions via a multiple Dynkin-Hunt formula. Zbl 1387.60121 Grigor’yan, Alexander; Kajino, Naotaka 7 2017 Yamabe type equations on graphs. Zbl 1351.35038 Grigor’yan, Alexander; Lin, Yong; Yang, Yunyan 87 2016 Kazdan-Warner equation on graph. Zbl 1366.58006 Grigor’yan, Alexander; Lin, Yong; Yang, Yunyan 81 2016 Surgery of the Faber-Krahn inequality and applications to heat kernel bounds. Zbl 1334.58019 Grigor’yan, Alexander; Saloff-Coste, Laurent 18 2016 On a cohomology of digraphs and Hochschild cohomology. Zbl 1353.05056 Grigor’yan, Alexander; Muranov, Yuri; Yau, Shing-Tung 10 2016 A lower bound for the number of negative eigenvalues of Schrödinger operators. Zbl 1356.53044 Grigor’yan, Alexander; Nadirashvili, Nikolai; Sire, Yannick 7 2016 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 35 2015 Cohomology of digraphs and (undirected) graphs. Zbl 1329.05132 Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung 23 2015 Heat kernel and Lipschitz-Besov spaces. Zbl 1327.35130 Grigor’yan, Alexander; Liu, Liguang 20 2015 Negative eigenvalues of two-dimensional Schrödinger operators. Zbl 1319.35128 Grigor’yan, Alexander; Nadirashvili, Nikolai 15 2015 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. 5 2015 On nonnegative solutions of the inequality \(\Delta u+u^{\sigma }\leq 0\) on Riemannian manifolds. Zbl 1296.58011 Grigor’yan, Alexander; Sun, Yuhua 43 2014 Upper bounds of heat kernels on doubling spaces. Zbl 1524.47050 Grigor’yan, Alexander; Hu, Jiaxin 39 2014 Homotopy theory for digraphs. Zbl 1312.05063 Grigor’yan, Alexander; Lin, Yong; Muranov, Yuri; Yau, Shing-Tung 33 2014 Isotropic Markov semigroups on ultra-metric spaces. Zbl 1322.60151 Bendikov, A. D.; Grigor’yan, A. A.; Pittet, Ch; Woess, W. 32 2014 Estimates of heat kernels for non-local regular Dirichlet forms. Zbl 1304.47058 Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 30 2014 Heat kernels and Green functions on metric measure spaces. Zbl 1293.35128 Grigor’yan, Alexander; Hu, Jiaxin 29 2014 Heat kernels on metric measure spaces. Zbl 1323.58018 Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 16 2014 Graphs associated with simplicial complexes. Zbl 1297.05269 Grigor’yan, A.; Muranov, Yu. V.; Yau, Shing-Tung 16 2014 Stochastic completeness of jump processes on metric measure spaces. Zbl 1318.28024 Grigor’yan, Alexander; Huang, Xueping 2 2014 Parabolicity and stochastic completeness of manifolds in terms of the Green formula. Zbl 1356.58007 Grigor’yan, Alexander; Masamune, Jun 27 2013 Stochastic completeness of symmetry Markov processes and volume growth. Zbl 1326.58020 Grigor’yan, Alexander 3 2013 Two-sided estimates of heat kernels on metric measure spaces. Zbl 1252.35148 Grigor’yan, Alexander; Telcs, Andras 71 2012 On the equivalence of parabolic Harnack inequalities and heat kernel estimates. Zbl 1281.58016 Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi 51 2012 On stochastic completeness of jump processes. Zbl 1408.60076 Grigor’yan, Alexander; Huang, Xueping; Masamune, Jun 47 2012 On a class of Markov semigroups on discrete ultra-metric spaces. Zbl 1260.60142 Bendikov, Alexander; Grigor’yan, Alexander; Pittet, Christophe 13 2012 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. 6 2012 Heat kernel estimates on a connected sum of two copies of \(\mathbb{R}^n\) along a surface of revolution. Zbl 1296.35081 Grigor’yan, Alexander; Ishiwata, Satoshi 1 2012 Yau’s work on heat kernels. Zbl 1271.58011 Grigor’yan, Alexander 3 2011 On the existence of positive solutions of semilinear elliptic inequalities on Riemannian manifolds. Zbl 1185.35344 Grigor’yan, Alexander; Kondratiev, Vladimir A. 20 2010 Comparison inequalities for heat semigroups and heat kernels on metric measure spaces. Zbl 1207.58021 Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 19 2010 Heat kernels on metric measure spaces with regular volume growth. Zbl 1217.58018 Grigor’yan, Alexander 19 2010 Heat kernel and analysis on manifolds. Zbl 1206.58008 Grigor’yan, Alexander 394 2009 Heat kernel upper bounds for jump processes and the first exit time. Zbl 1158.60039 Barlow, Martin T.; Grigor’yan, Alexander; Kumagai, Takashi 67 2009 Heat kernel on manifolds with ends. Zbl 1239.58016 Grigor’yan, Alexander; Saloff-Coste, Laurent 38 2009 Heat kernels on metric spaces with doubling measure. Zbl 1197.35129 Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 21 2009 Volume growth and escape rate of Brownian motion on a Cartan-Hadamard manifold. Zbl 1167.58019 Grigor’yan, Alexander; Hsu, Elton 12 2009 Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces. Zbl 1154.47034 Grigor’yan, Alexander; Hu, Jiaxin 33 2008 On the dichotomy in the heat kernel two sided estimates. Zbl 1162.47037 Grigor’yan, Alexander; Kumagai, Takashi 18 2008 Lower estimates for a perturbed Green function. Zbl 1158.35022 Grigor’yan, Alexander; Hansen, Wolfhard 11 2008 Obtaining upper bounds of heat kernels from lower bounds. Zbl 1148.58013 Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 6 2008 Heat kernels on weighted manifolds and applications. Zbl 1106.58016 Grigor’yan, Alexander 115 2006 Stability results for Harnack inequalities. Zbl 1115.58024 Grigor’yan, Alexander; Saloff-Coste, Laurent 63 2005 The discrete integral maximum principle and its applications. Zbl 1096.60023 Coulhon, Thierry; Grigor’yan, Alexander; Zucca, Fabio 24 2005 Eigenvalues of elliptic operators and geometric applications. Zbl 1061.58027 Grigor’yan, Alexander; Netrusov, Yuri; Yau, Shing-Tung 44 2004 Surveys in differential geometry. Vol. IX: Eigenvalues of Laplacians and other geometric operators. Zbl 1050.53002 4 2004 Heat kernels on metric measure spaces and an application to semilinear elliptic equations. Zbl 1018.60075 Grigor’yan, Alexander; Hu, Jiaxin; Lau, Ka-Sing 76 2003 Heat kernels and function theory on metric measure spaces. Zbl 1048.58021 Grigor’yan, Alexander 67 2003 On isoperimetric profiles of product spaces. Zbl 1085.53027 Coulhon, Thierry; Grigor’yan, Alexander; Levin, Daniel 14 2003 Isoperimetric properties of higher eigenvalues of elliptic operators. Zbl 1042.58017 Grigor’yan, Alexander; Yau, Shing-Tung 12 2003 Pointwise estimates for transition probabilities of random walks on infinite graphs. Zbl 1048.60081 Coulhon, Thierry; Grigor’yan, Alexander 8 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 5 2003 Recurrence and transience of branching diffusion processes on Riemannian manifolds. Zbl 1014.60081 Grigor’yan, Alexander; Kelbert, Mark 4 2003 Harnack inequalities and sub-Gaussian estimates for random walks. Zbl 1011.60021 Grigor’yan, A.; Telcs, A. 44 2002 Dirichlet heat kernel in the exterior of a compact set. Zbl 1037.58018 Grigor’yan, Alexander; Saloff-Coste, Laurent 41 2002 Hitting probabilities for Brownian motion on Riemannian manifolds. Zbl 1042.58022 Grigor’yan, Alexander; Saloff-Coste, Laurent 30 2002 Sub-Gaussian estimates of heat kernels on infinite graphs. Zbl 1010.35016 Grigor’yan, Alexander; Telcs, Andras 48 2001 Manifolds and graphs with slow heat kernel decay. Zbl 1003.58025 Barlow, Martin; Coulhon, Thierry; Grigor’yan, Alexander 37 2001 A geometric approach to on-diagonal heat kernel lower bounds on groups. Zbl 1137.58307 Coulhon, Thierry; Grigor’yan, Alexander; Pittet, Christophe 26 2001 Heat kernels on manifolds, graphs and fractals. Zbl 1057.58010 Grigor’yan, Alexander 12 2001 XIIIth international congress on mathematical physics. Proceedings of the ICMP 2000, Imperial College, London, Great Britain, July 17–22, 2000. Zbl 0994.00023 3 2001 Asymptotic separation for independent trajectories of Markov processes. Zbl 0973.58020 Grigor’yan, Alexander; Kelbert, Mark 1 2001 Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs. Zbl 1001.58022 Chung, Fan; Grigor’yan, Alexander; Yau, Shing-Tung 31 2000 On Hardy-Littlewood inequality for Brownian motion on Riemannian manifolds. Zbl 1026.58028 Grigor’yan, Alexander; Kelbert, Mark 8 2000 Mathematical physics 2000. International congress, London, GB, 2000. Zbl 0949.00037 6 2000 Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds. Zbl 0927.58019 Grigor’yan, Alexander 435 1999 Estimates of heat kernels on Riemannian manifolds. Zbl 0985.58007 Grigor’yan, Alexander 72 1999 ...and 39 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,026 Authors 63 Grigor’yan, Alexander Asaturovich 40 Punzo, Fabio 36 Saloff-Coste, Laurent 35 Kumagai, Takashi 25 Chen, Zhen-Qing 25 Hua, Bobo 24 de Lima, Henrique F. 22 Wang, Jian 19 Keller, Matthias 18 Grillo, Gabriele 18 Lin, Yong 18 Palmer, Vicente 17 Hu, Jiaxin 16 Coulhon, Thierry 16 Pigola, Stefano 16 Sun, Yuhua 16 Teplyaev, Alexander 15 Barlow, Martin T. 15 Bendikov, Alexander D. 15 Rigoli, Marco 15 Setti, Alberto G. 14 Cunha, Antonio Wilson 14 Güneysu, Batu 14 Muratori, Matteo 13 Gimeno, Vicent 13 Lenz, Daniel H. 13 Bessa, Gregório Pacelli 13 Velásquez, Marco Antonio Lázaro 13 Wojciechowski, Radosław Krzysztof 12 Huang, Xueping 12 Kim, Panki 12 Mari, Luciano 12 Masamune, Jun 12 Mazepa, Elena Alekseevna 12 Muranov, Yuriĭ Vladimirovich 12 Murugan, Mathav Kishore 12 Ouhabaz, El Maati 11 Baudoin, Fabrice 11 Carron, Gilles 11 Duong, Xuan Thinh 11 Lau, Kasing 11 Yan, Lixin 11 Yang, Dachun 10 Bernicot, Frédéric 10 Ishige, Kazuhiro 10 Li, Pengtao 10 Liu, Yang 10 Shanmugalingam, Nageswari 10 Shiozawa, Yuichi 10 Sikora, Adam 10 Telcs, András 10 Wang, Feng-Yu 10 Wu, Yiting 10 Yau, Shing-Tung 10 Zhang, Qi-Shuhuason 9 Alías, Luis J. 9 Chen, Li 9 de Lima, Eudes Leite 9 Kajino, Naotaka 9 Mhaskar, Hrushikesh N. 9 Milatovic, Ognjen 9 Monticelli, Dario Daniele 9 Pittet, Christophe 9 Schmidt, Marcel 9 Tian, Canrong 9 Verbitsky, Igor E. 9 Yang, Yunyan 9 Zheng, Tianyi 8 Alonso-Ruiz, Patricia 8 Colbois, Bruno 8 Ganguly, Debdip 8 Hinz, Michael 8 Hurtado, Ana 8 Kaßmann, Moritz 8 Li, Hongquan 8 Markvorsen, Steen 8 Papageorgiou, Effie G. 8 Qiu, Hua 8 Takeda, Masayoshi 8 Thalmaier, Anton 8 van den Berg, Michiel 8 Xiao, Jie 8 Yang, Qiaohua 7 Auscher, Pascal 7 Bass, Richard F. 7 Berchio, Elvise 7 Cao, Shiping 7 Chen, Peng 7 Colli, Pierluigi 7 Devyver, Baptiste 7 Frey, Dorothee 7 Fukao, Takeshi 7 Ge, Huabin 7 Gu, Qingsong 7 Hansen, Wolfhard 7 Holopainen, Ilkka 7 Liu, Yu 7 Losev, Alexander Georgievoch 7 Lu, Guozhen 7 Maz’ya, Vladimir Gilelevich ...and 1,926 more Authors all top 5 Cited in 361 Serials 93 Journal of Functional Analysis 79 Potential Analysis 77 The Journal of Geometric Analysis 71 Journal of Mathematical Analysis and Applications 53 Calculus of Variations and Partial Differential Equations 52 Transactions of the American Mathematical Society 44 Advances in Mathematics 44 Mathematische Annalen 42 Nonlinear Analysis. 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