31 citations · 110 across the 36 of their papers we have counts for
4 papers · 1 filter
Ricci curvature, entropy and optimal transport
Shin-Ichi Ohta
This is the lecture notes on the interplay between optimal transport and Riemannian geometry. On a Riemannian manifold, the convexity of entropy along optimal transport in the spac…
Non-contraction of heat flow on Minkowski spaces
Shin-ichi Ohta, Karl-Theodor Sturm
We study contractivity properties of gradient flows for functions on normed spaces or, more generally, on Finsler manifolds. Contractivity of the flows turns out to be equivalent t…
Heat flow on Alexandrov spaces
Nicola Gigli, Kazumasa Kuwada, Shin-ichi Ohta
We prove that on compact Alexandrov spaces with curvature bounded below the gradient flow of the Dirichlet energy in the -space produces the same evolution as the gradient flo…
Displacement convexity of generalized relative entropies
Shin-ichi Ohta, Asuka Takatsu
We investigate the -relative entropy, which stems from the Bregman divergence, on weighted Riemannian and Finsler manifolds. We prove that the displacement -convexity of the…