40 citations · 126 across the 29 of their papers we have counts for
12 papers · 1 filter
-entropy formulas and Langevin deformation on the -Wasserstein space over Riemannian manifolds
Rong Lei, Xiang-Dong Li, Yu-Zhao Wang
We first prove the -entropy formula and rigidity theorem for the geodesic flow on the -Wasserstein space over a complete Riemannian manifold with bounded geometry condition…
Langevin deformation for Rényi entropy on Wasserstein space over Riemannian manifolds
Rong Lei, Songzi Li, Xiang-Dong Li
We introduce the Langevin deformation for the Rényi entropy on the -Wasserstein space over or a Riemannian manifold, which interpolates between the porous mediu…
On the Navier-Stokes equations and the Hamilton-Jacobi-Bellman equation on the group of volume preserving diffeomorphisms
Xiang-Dong Li, Guoping Liu
In this paper, we give a new derivation of the incompressible Navier-Stokes equations on a compact Riemannian manifold via the Bellman dynamic programming principle on the infi…
Stochastic differential equations and stochastic parallel translations in the Wasserstein space
Hao Ding, Shizan Fang, Xiang-dong Li
We will develop some elements in stochastic analysis in the Wasserstein space over a compact Riemannian manifold , such as intrinsic It formulae, stochastic…
Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces
Kazumasa Kuwada, Xiang-Dong Li
By means of a space-time Wasserstein control, we show the monotonicity of the W-entropy functional in time along heat flows on possibly singular metric measure spaces with non-nega…
-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds
Songzi Li, Xiang-Dong Li
We introduce Perelman's -entropy and prove the -entropy formula along the geodesic flow on the -Wasserstein space over compact Riemannian manifolds equipped with Otto's…