212 citations · 625 across the 54 of their papers we have counts for
4 papers · 1 filter
Sub-Riemannian Ricci curvature via generalized Gamma calculus
Qi Feng, Wuchen Li
We derive sub-Riemannian Ricci curvature tensor for sub-Riemannian manifolds. We provide examples including the Heisenberg group, displacement group, and Martinet sub-Riemannian st…
Hessian metric via transport information geometry
Wuchen Li
We propose to study the Hessian metric of a functional on the space of probability measures endowed with the Wasserstein -metric. We name it transport Hessian metric, which cont…
Entropy dissipation for degenerate stochastic differential equations via sub-Riemannian density manifold
Qi Feng, Wuchen Li
We study the dynamical behaviors of degenerate stochastic differential equations (SDEs). We select an auxiliary Fisher information functional as the Lyapunov functional. Using gene…
Transport information geometry I: Riemannian calculus on probability simplex
Wuchen Li
We formulate the Riemannian calculus of the probability set embedded with -Wasserstein metric. This is an initial work of transport information geometry. Our investigation sta…