69 citations · 150 across the 21 of their papers we have counts for
21 papers
Ricci Flow and Gromov Almost Flat Manifolds
Eric Chen, Guofang Wei, Rugang Ye
We employ the Ricci flow to derive a new theorem about Gromov almost flat manifolds, which generalizes and strengthens the celebrated Gromov--Ruh Theorem. In our theorem, the condi…
A Note On Obata's Rigidity Theorem I
Guoqiang Wu, Rugang Ye
In this note we present various extensions of Obata's rigidity theorem concerning the Hessian of a function on a Riemannian manifold. They include general rigidity theorems for the…
Existence, Convergence and Limit Map of the Laplacian Flow
Feng Xu, Rugang Ye
We prove short time existence and uniqueness of the Laplacian flow starting at an arbitrary closed -structure. We establish long time existence and convergence of the Laplacia…
Entropy Functionals, Sobolev Inequalities and kappa-Noncollapsing Estimates along the Ricci Flow
Rugang Ye
In this survey we review Hamilton's entropy and Perelman's entropy, and provide motivations for these concepts. Then we review recent results on the logarithmic Sobolev inequality,…
Sobolev Inequalities, Riesz Transforms and the Ricci Flow
Rugang Ye
In this paper we study the problem of deriving further Sobolev inequalities from a given Sobolev inequality. We use several different methods, including Bessel potentials and Riesz…
The logarithmic Sobolev inequality along the Ricci flow
Rugang Ye
We derive a logarithmic Sobolev inequality along the Ricci flow without any restriction on time, which depends only on the initial metric via rudimentary geometric data, assuming o…