Karl-Theodor Sturm

On the geometry of metric measure spaces. II

AbstractWe introduce and analyze lower (Ricci) curvature bounds

ON THE GEOMETRY DEFINED BY DIRICHLET FORMS

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entropic measure and Wasserstein diffusion.

 ⩾ K for metric measure spaces

New Directions in Dirichlet Forms

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Measures charging no polar sets and additive functionals of Brownian motion

. Our definition is based on convexity properties of the relative entropy

Nonlinear Markov operators associated with symmetric Markov kernels and energy minimizing maps between singular spaces

Ent{\left( { \cdot \left| m \right.} \right)}

Nonlinear Markov Operators, Discrete Heat Flow, and Harmonic Maps Between Singular Spaces

regarded as a function on the L2-Wasserstein space of probability measures on the metric space

Optimal transport from Lebesgue to Poisson

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Expectations and martingales in metric spaces

. Among others, we show that

Is a diffusion process determined by its intrinsic metric

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