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Alexander Grigor'yan

Alexander Grigor'yan

D-Index & Metrics

Mathematics

D-Index
51
Citations
9214
World Ranking
1035
National Ranking
54

Overview

Alexander Grigor'yan is a researcher affiliated with Bielefeld University in Germany, with a focus on the field of Mathematics. Their work predominantly spans applied mathematics, mathematical physics, computational theory and mathematics, geometry and topology, and molecular biology.

The scientist's research covers a range of advanced mathematical topics and theories. Key themes in their publications include:

  • Geometric Analysis and Curvature Flows
  • Nonlinear Partial Differential Equations
  • Topological and Geometric Data Analysis
  • Advanced Mathematical Modeling in Engineering
  • Advanced Mathematical Theories
  • Homotopy and Cohomology in Algebraic Topology
  • Spectral Theory in Mathematical Physics

Alexander Grigor'yan has contributed to several recent academic papers, illustrating their engagement with both theoretical and applied mathematical sciences. Notable recent publications include:

  • "Path Complexes and their Homologies," 2020, Journal of Mathematical Sciences
  • "Pointwise estimates of solutions to nonlinear equations for nonlocal operators," 2020, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
  • "Anaerobic microbial communities and their potential for bioenergy production in heavily biodegraded petroleum reservoirs," 2020, Environmental Microbiology
  • "Heat Kernels and Besov Spaces Associated with Second Order Divergence Form Elliptic Operators," 2020, Journal of Fourier Analysis and Applications
  • "Heat kernels and Besov spaces on metric measure spaces," 2022, Journal d Analyse Mathématique

The researcher frequently publishes in several scientific venues, with multiple contributions to:

  • arXiv (Cornell University)
  • Journal of Functional Analysis
  • Microbiology Resource Announcements
  • Journal of Mathematical Sciences
  • Environmental Microbiology

Collaboration is also an important aspect of Alexander Grigor'yan's profile, evident from frequent co-authorship with other scholars, including:

  • Shing-Tung Yau
  • Alexander Bendikov
  • Stanislav Molchanov
  • Yong Lin
  • Yu. V. Muranov

Overall, the scientist's work is situated at the intersection of pure and applied mathematics, with multidisciplinary applications reaching into biological and physical sciences.

Best Publications

  • Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds

    Alexander Grigor’yan

  • Heat Kernel and Analysis on Manifolds

    Alexander Grigor’yan

  • THE HEAT EQUATION ON NONCOMPACT RIEMANNIAN MANIFOLDS

    A A Grigor'yan

  • HEAT KERNEL UPPER BOUNDS ON A COMPLETE NON-COMPACT MANIFOLD

    Alexander Grigor'yan

  • Surveys in differential geometry

    Alexander Grigor'yan;Shing-Tung Yau

  • Heat kernels on metric measure spaces and an application to semilinear elliptic equations

    Alexander Grigor’yan;Jiaxin Hu;Ka-Sing Lau

  • THE HEAT KERNEL ON HYPERBOLIC SPACE

    Alexander Grigor'yan;Masakazu Noguchi

  • TWO-SIDED ESTIMATES OF HEAT KERNELS ON METRIC MEASURE SPACES

    Alexander Grigor’yan;Andras Telcs

  • Yamabe type equations on graphs

    Alexander Grigor'yan;Yong Lin;Yunyan Yang

  • Existence of positive solutions to some nonlinear equations on locally finite graphs

    Alexander Grigor’yan;Yong Lin;YunYan Yang

  • Kazdan–Warner equation on graph

    Alexander Grigor’yan;Yong Lin;Yunyan Yang

  • Estimates of heat kernels on Riemannian manifolds

    Unknown

  • Random Walks on Graphs with Regular Volume Growth

    T. Coulhon;A. Grigoryan

  • Sub-Gaussian estimates of heat kernels on infinite graphs

    Alexander Grigor'yan;Andras Telcs

  • On the equivalence of parabolic Harnack inequalities and heat kernel estimates

    Martin T. Barlow;Alexander Grigor'yan;Takashi Kumagai

  • Manifolds and graphs with slow heat kernel decay

    Martin Barlow;Thierry Coulhon;Alexander Grigor’yan

  • Eigenvalues of elliptic operators and geometric applications

    A. Grigor’yan;Y. Netrusov;S.-T. Yau

  • Stability results for Harnack inequalities

    Alexander Grigor'yan;Laurent Saloff-Coste

  • Mathematical Physics 2000

    A. S. Fokas;A. Grigoryan;T. W. B. Kibble;B. Zegarlinski

  • Heat kernel upper bounds for jump processes and the first exit time

    Martin T. Barlow;Alexander Grigor'yan;Takashi Kumagai

  • Harnack inequalities and sub-Gaussian estimates for random walks

    A. Grigor'yan;A. Telcs

  • Isotropic Markov semigroups on ultra-metric spaces

    Alexander Davidovich Bendikov;Alexander Asaturovich Grigor'Yan;Christophe Pittet;Wolfgang Woess

Frequent Co-Authors

Shing-Tung Yau
Shing-Tung Yau Tsinghua University
Thierry Coulhon
Thierry Coulhon PSL University
Laurent Saloff-Coste
Laurent Saloff-Coste Cornell University
Ka-Sing Lau
Ka-Sing Lau Chinese University of Hong Kong
Martin T. Barlow
Martin T. Barlow University of British Columbia
Fan Chung
Fan Chung University of California, San Diego
Nikolai Nadirashvili
Nikolai Nadirashvili Aix-Marseille University
Michael Röckner
Michael Röckner Bielefeld University
Peter B. Gilkey
Peter B. Gilkey University of Oregon
Wolfgang Woess
Wolfgang Woess Graz University of Technology

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