The logarithmic entropy formula for the linear heat equation on Riemannian manifolds |
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Authors: | Jia-Yong Wu |
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Institution: | Department of Mathematics, Shanghai Maritime University, Haigang Avenue 1550, Shanghai 201306, PR China |
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Abstract: | In this paper we introduce a new logarithmic entropy functional for the linear heat equation on complete Riemannian manifolds and prove that it is monotone decreasing on complete Riemannian manifolds with nonnegative Ricci curvature. Our results are simpler version, without Ricci flow, of R.-G. Ye’s recent result (arXiv:math.DG/0708.2008). As an application, we apply the monotonicity of the logarithmic entropy functional of heat kernels to characterize Euclidean space. |
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Keywords: | 35P15 58J50 53C21 |
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