most citedThe logarithmic Sobolev inequality along the Ricci flow

69 citations · 87 across the 6 of their papers we have counts for

collaborators

8 papers

math.DG2007★ 10 cited

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,…

math.DG2007

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…

math.DG2007★ 69 cited

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…

math.DG2007

The logarithmic Sobolev inequality along the Ricci flow: the case

Rugang Ye

We extend our previous results on the logarithmic Sobolev inequality along the Ricci flow in the case to the case .

math.DG2007★ 8 cited

The logarithmic Sobolev inequality along the Ricci flow in dimension 2

Rugang Ye

In this paper we present our results on the logarithmic Sobolev inequality along the Ricci flow in dimension 2.

math.DG2007

A Neumann Type Maximum Principle for the Laplace Operator on Compact Riemannian Manifolds

Guofang Wei, Rugang Ye

In this paper we present a proof of a Neumann type maximum principle for the Laplace operator on compact Riemannian manifolds. A key p oint is the simple geometric nature of the co…