The entropy formula for linear heat equation

Details The entropy formula for linear heat equation The entropy formula for linear heat equation

2003-06-09

arxiv.org/abs/math/0306147v2

Mathematics

Differential Geometry

to appear in Jour. Geom. Anal

Scientific paper

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.

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