The entropy formula for linear heat equation

2003/06/09 by Lei Ni, Ni, Lei · 4 citations
Mathematics · #58G11 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:58G11

paper · pdf · doi:10.48550/arxiv.math/0306147

to appear in Jour. Geom. Anal

arxiv created 2003/09/25 · arxiv updated 2009/11/30

Abstract

We derive the entropy formula for the linear heat equaiton on complete Riemannian manifolds with nonnegative Ricci curvature. As applications, we study the relation between the value of entropy and the volume of balls of various scales. The results are simpler version, without Ricci flow, of Perelman's recent results on volume non-collapsing.

Cited by

• Monotonicity of Perelman W-Entropy of Mean Curvature Flow
• Is a complete Riemannian manifold with positively pinched Ricci curvature compact
• Fenchel-Willmore and Sobolev-type inequalities for submanifolds in non-negatively curved manifolds
• On the rigidity of manifolds with respect to Gagliardo-Nirenberg inequalities

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