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On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces

Inventiones mathematicae, 2015-09, Vol.201 (3), p.993-1071

2015

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On the geometry of metric measure spaces. II

Acta mathematica, 2006-07, Vol.196 (1), p.133-177

STURM, Karl-Theodor

2006

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Ricci tensor for diffusion operators and curvature-dimension inequalities under conformal transformations and time changes

Journal of functional analysis, 2018-08, Vol.275 (4), p.793-829

Sturm, Karl-Theodor

2018

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Heat Flow on Time‐Dependent Metric Measure Spaces and Super‐Ricci Flows

Communications on pure and applied mathematics, 2018-12, Vol.71 (12), p.2500-2608

2018

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Localization and tensorization properties of the curvature-dimension condition for metric measure spaces

Journal of functional analysis, 2010-07, Vol.259 (1), p.28-56

2010

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Gradient flows for semiconvex functions on metric measure spaces -- existence, uniqueness, and Lipschitz continuity

Proceedings of the American Mathematical Society, 2018-09, Vol.146 (9), p.3985-3994

STURM, KARL-THEODOR

2018

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Heat flow on Finsler manifolds

Communications on pure and applied mathematics, 2009-10, Vol.62 (10), p.1386-1433

2009

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Functional inequalities for the heat flow on time‐dependent metric measure spaces

Journal of the London Mathematical Society, 2021-09, Vol.104 (2), p.926-955

2021

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Heat flow with Dirichlet boundary conditions via optimal transport and gluing of metric measure spaces

Calculus of variations and partial differential equations, 2020-08, Vol.59 (4), Article 117

2020

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Super-Ricci flows for metric measure spaces

Journal of functional analysis, 2018-12, Vol.275 (12), p.3504-3569

Sturm, Karl-Theodor

2018

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Transport inequalities, gradient estimates, entropy and Ricci curvature

Communications on pure and applied mathematics, 2005-07, Vol.58 (7), p.923-940

2005

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Curvature-dimension conditions under time change

Annali di matematica pura ed applicata, 2022, Vol.201 (2), p.801-822

2022

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On the geometry of metric measure spaces

Acta mathematica, 2006-07, Vol.196 (1), p.65-131

Sturm, Karl-Theodor

2006

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The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces

Memoirs of the American Mathematical Society, 2023-10, Vol.290 (1443)

Sturm, Karl-Theodor

2023

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Correction to “On the geometry of metric measure spaces. I”

Acta mathematica, 2023, Vol.231 (2), p.387-390

Sturm, Karl-Theodor

2023

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Distribution-Valued Ricci Bounds for Metric Measure Spaces, Singular Time Changes, and Gradient Estimates for Neumann Heat Flows

Geometric and functional analysis, 2020-12, Vol.30 (6), p.1648-1711

Sturm, Karl-Theodor

2020

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Non-branching geodesics and optimal maps in strong CD(K,∞)-spaces

Calculus of variations and partial differential equations, 2014, Vol.50 (3-4), p.831-846

2014

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Mass transportation and rough curvature bounds for discrete spaces

Journal of functional analysis, 2009-05, Vol.256 (9), p.2944-2966

2009

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

The Journal of geometric analysis, 2016-10, Vol.26 (4), p.2914-2929

2016

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Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds

Journal de mathématiques pures et appliquées, 2021-03, Vol.147, p.60-97

2021

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Non-Contraction of Heat Flow on Minkowski Spaces

Archive for rational mechanics and analysis, 2012-06, Vol.204 (3), p.917-944

2012

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Remarks about synthetic upper Ricci bounds for metric measure spaces

Tôhoku mathematical journal, 2021-01, Vol.73 (4)

Sturm, Karl-Theodor

2021

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Rigidity of cones with bounded Ricci curvature

Journal of the European Mathematical Society : JEMS, 2021-01, Vol.23 (1), p.219-235

2021

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

Advances in mathematics (New York. 1965), 2014-02, Vol.252, p.429-448

2014

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Localization and tensorization properties of the curvature-dimension condition for metric measure spaces, II

Journal of functional analysis, 2011-06, Vol.260 (12), p.3718-3725

2011

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On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces

On the geometry of metric measure spaces. II

Ricci tensor for diffusion operators and curvature-dimension inequalities under conformal transformations and time changes

Heat Flow on Time‐Dependent Metric Measure Spaces and Super‐Ricci Flows

Localization and tensorization properties of the curvature-dimension condition for metric measure spaces

Gradient flows for semiconvex functions on metric measure spaces -- existence, uniqueness, and Lipschitz continuity

Heat flow on Finsler manifolds

Functional inequalities for the heat flow on time‐dependent metric measure spaces

Heat flow with Dirichlet boundary conditions via optimal transport and gluing of metric measure spaces

Super-Ricci flows for metric measure spaces

Transport inequalities, gradient estimates, entropy and Ricci curvature

Curvature-dimension conditions under time change

On the geometry of metric measure spaces

The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces

Correction to “On the geometry of metric measure spaces. I”

Distribution-Valued Ricci Bounds for Metric Measure Spaces, Singular Time Changes, and Gradient Estimates for Neumann Heat Flows

Non-branching geodesics and optimal maps in strong CD(K,∞)-spaces

Mass transportation and rough curvature bounds for discrete spaces

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

Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds

Non-Contraction of Heat Flow on Minkowski Spaces

Remarks about synthetic upper Ricci bounds for metric measure spaces

Rigidity of cones with bounded Ricci curvature

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

Localization and tensorization properties of the curvature-dimension condition for metric measure spaces, II

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