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Karl-Theodor Sturm

Karl-Theodor Sturm

D-Index & Metrics

Mathematics

D-Index
30
Citations
7616
World Ranking
3424
National Ranking
211

Overview

Karl-Theodor Sturm is affiliated with the University of Bonn in Germany and specializes in research within the broad field of mathematics, with a particular focus on applied mathematics, geometry and topology, and mathematical physics.

Their research encompasses several subfields, including:

  • Applied Mathematics
  • Geometry and Topology
  • Astronomy and Astrophysics
  • Mathematical Physics
  • Computational Mechanics

Main topics addressed in their work include:

  • Geometric Analysis and Curvature Flows
  • Geometry and Complex Manifolds
  • Advanced Differential Geometry Research
  • Nonlinear Partial Differential Equations
  • Stochastic Processes and Statistical Mechanics
  • Point Processes and Geometric Inequalities
  • Cosmology and Gravitation Theories

Karl-Theodor Sturm has contributed to multiple publication venues, with notable frequency in:

  • arXiv (Cornell University)
  • Journal of the London Mathematical Society
  • Calculus of Variations and Partial Differential Equations
  • Oberwolfach Reports
  • Memoirs of the American Mathematical Society

Some recent papers authored or co-authored include:

  • The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces, 2023, Memoirs of the American Mathematical Society
  • Remarks about synthetic upper Ricci bounds for metric measure spaces, 2021, Tohoku Mathematical Journal
  • Heat flow with Dirichlet boundary conditions via optimal transport and gluing of metric measure spaces, 2020, Calculus of Variations and Partial Differential Equations
  • Functional inequalities for the heat flow on time-dependent metric measure spaces, 2021, Journal of the London Mathematical Society
  • Tamed spaces - Dirichlet spaces with distribution-valued Ricci bounds, 2022, Journal de Mathématiques Pures et Appliquées

Frequent collaborators in their research include:

  • Eva Kopfer
  • Lorenzo Dello Schiavo
  • Matthias Erbar
  • Ronan Herry
  • Chiara Rigoni

Best Publications

  • On the geometry of metric measure spaces

    Unknown

  • On the geometry of metric measure spaces. II

    Karl-Theodor Sturm

  • Transport inequalities, gradient estimates, entropy and Ricci curvature

    Max-K. von Renesse;Max-K. von Renesse;Karl-Theodor Sturm

  • ON THE EQUIVALENCE OF THE ENTROPIC CURVATURE-DIMENSION CONDITION AND BOCHNER'S INEQUALITY ON METRIC MEASURE SPACES

    Matthias Erbar;Kazumasa Kuwada;Karl Theodor Sturm

  • Probability Measures on Metric Spaces of Nonpositive Curvature

    Unknown

  • Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.

    Karl-Theodor Sturm

  • Analysis on local Dirichlet spaces. III. The parabolic Harnack inequality

    K. T. Sturm

  • Analysis on local Dirichlet spaces. II. Upper Gaussian estimates for the fundamental solutions of parabolic equations

    Karl-Theodor Sturm

  • Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces

    Kathrin Bacher;Karl-Theodor Sturm

  • Heat flow on Finsler manifolds

    Shin-ichi Ohta;Karl-Theodor Sturm

  • Non-branching geodesics and optimal maps in strong \(CD(K,\infty )\)-spaces

    Tapio Rajala;Karl-Theodor Sturm

  • Bochner–Weitzenböck formula and Li–Yau estimates on Finsler manifolds

    Shin-ichi Ohta;Karl-Theodor Sturm

  • Diffusion processes and heat kernels on metric spaces

    K. T. Sturm

  • Mass transportation and rough curvature bounds for discrete spaces

    Anca-Iuliana Bonciocat;Karl-Theodor Sturm

  • Entropic measure and Wasserstein diffusion

    Max-K. von Renesse;Karl-Theodor Sturm

  • Convex functionals of probability measures and nonlinear diffusions on manifolds

    Karl-Theodor Sturm

  • On the Lp-Spectrum of Uniformly Elliptic Operators on Riemannian Manifolds

    K.T. Sturm

  • The space of spaces: curvature bounds and gradient flows on the space of metric measure spaces

    Karl-Theodor Sturm

  • Optimal Maps and Exponentiation on Finite-Dimensional Spaces with Ricci Curvature Bounded from Below

    Nicola Gigli;Nicola Gigli;Tapio Rajala;Karl-Theodor Sturm

  • Local curvature-dimension condition implies measure-contraction property

    Fabio Cavalletti;Karl-Theodor Sturm

  • ON THE GEOMETRY DEFINED BY DIRICHLET FORMS

    Karl-Theodor Sturm

  • Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature

    Karl-Theodor Sturm

  • New Directions in Dirichlet Forms

    Jürgen Jost;Wilfrid Kendall;Umberto Mosco;Michael Röckner

Frequent Co-Authors

Michael Röckner
Michael Röckner Bielefeld University
Jürgen Jost
Jürgen Jost Max Planck Institute for Mathematics in the Sciences
Nicola Gigli
Nicola Gigli International School for Advanced Studies
Takashi Kumagai
Takashi Kumagai Waseda University
Martin Rumpf
Martin Rumpf University of Bonn
Laurent Saloff-Coste
Laurent Saloff-Coste Cornell University
Felix Otto
Felix Otto Max Planck Institute for Mathematics in the Sciences

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