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18 February 2025
 
  » arxiv » 1109.0136

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The logarithmic entropy formula for the linear heat equation on Riemannian manifolds
Jia-Yong Wu ;
Date 1 Sep 2011
AbstractIn this note we introduce a new logarithmic entropy functional for the linear heat equation on closed Riemannian manifolds and prove that it is monotone decreasing along the heat equation on closed manifolds with nonnegative Ricci curvature. Our results are simpler version, without Ricci flow, of the R.-G. Ye’s recent result(arXiv:0708.2008). As an application, we apply the monotonicity of the logarithmic entropy functional to characterize Euclidean space.
Source arXiv, 1109.0136
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