4 citations · 5 across the 2 of their papers we have counts for
2 papers
math.CA2010★ 1 cited
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…
math.DG2010★ 4 cited
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…