The entropy formula for linear heat equation

Lei Ni

The entropy formula for linear heat equation

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arxiv math/0306147 v2 pith:D6EU5F7A submitted 2003-06-09 math.DG

Lei Ni This is my paper · ORCID

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keywords entropyformulaheatlinearresultsriccivolumeapplications

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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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Heat kernel geometry and Gromov's volume growth conjecture
math.DG 2026-08 conditional novelty 8.0 of 10

Gromov's volume growth conjecture is proven: Ric>=0 and Scal>=1 on a complete noncompact n-manifold force Vol(B(p,R))<=C_n R^(n-2) for all centers and radii.

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