A mean-value lemma and applications
摘要
We control the gap between the mean value of a function on a submanifold (or a point), and its mean value on any tube around the submanifold (in fact, we give the exact value of the second derivative of the gap). We apply this formula to obtain comparison theorems between eigenvalues of the Laplace-Beltrami operator, and then to compute the first three terms of the asymptotic time-expansion of a heat diffusion process on convex polyhedrons in euclidean spaces of arbitrary dimension. We also write explicit bounds for the remainder term of the above expansion, which hold for all values of time. The results of this paper have been announced, without proof, in
引用本文（GB/T 7714）
Alessandro Savo. A mean-value lemma and applications[J]. Bulletin de la Société mathématique de France, 2001.
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