40 citations · 90 across the 18 of their papers we have counts for
8 papers · 1 filter
Liouville theorem for -harmonic maps under non-negative -Ricci curvature for non-positive
Kazuhiro Kuwae, Songzi Li, Xiangdong Li +1
Let be a -vector field on an -dimensional complete Riemannian manifold . We prove a Liouville theorem for -harmonic maps satisfying various growth conditions…
On the Renyi entropy power and the Gagliardo-Nirenberg-Sobolev inequality on Riemannian manifolds
Songzi Li, Xiang-Dong Li
In this paper, we prove the concavity of the Renyi entropy power for nonlinear diffusion equation (NLDE) associated with the Laplacian and the Witten Laplacian on compact Riemannia…
-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds
Songzi Li, Xiang-Dong Li
In this survey paper, we give an overview of our recent works on the study of the -entropy for the heat equation associated with the Witten Laplacian on super-Ricci flows and th…
Hamilton differential Harnack inequality and -entropy for Witten Laplacian on Riemannian manifolds
Songzi Li, Xiang-Dong Li
In this paper, we prove the Hamilton differential Harnack inequality for positive solutions to the heat equation of the Witten Laplacian on complete Riemannian manifolds with the $…
On Harnack inequalities for Witten Laplacian on Riemannian manifolds with super Ricci flows
Songzi Li, Xiang-Dong Li
In this paper, we prove the Li-Yau type Harnack inequality and Hamilton type dimension free Harnack inequality for the heat equation associated with the time depe…
-entropy, super Perelman Ricci flows and -Ricci solitons
Songzi Li, Xiang-Dong Li
In this paper, we prove the characterization of the -super Perelman Ricci flows by various functional inequalities and gradient estimate for the heat semigroup generat…
Harnack inequalities and -entropy formula for Witten Laplacian on Riemannian manifolds with -super Perelman Ricci flow
Songzi Li, Xiang-Dong Li
In this paper, we prove logarithmic Sobolev inequalities and derive the Hamilton Harnack inequality for the heat semigroup of the Witten Laplacian on complete Riemannian manifolds…
-entropy formula for the Witten Laplacian on manifolds with time dependent metrics and potentials
Songzi Li, Xiang-Dong Li
In this paper, we develop a new approach to prove the -entropy formula for the Witten Laplacian via warped product on Riemannian manifolds and give a natural geometric interpret…