紧致黎曼流形上拉普拉斯算子的诺伊曼型最大值原理
微分几何
2007-11-12 v2
摘要
在本文中，我们给出了紧致黎曼流形上拉普拉斯算子的一个诺伊曼型最大值原理的证明。一个关键点是该最大值原理的先验估计中常数的简单几何性质。特别地，该最大值原理可应用于 Ricci 曲率有下界且直径有上界的流形，从而得到不依赖于体积正下界的最大值估计。
引用
@article{arxiv.math/0703505,
title = {A Neumann Type Maximum Principle for the Laplace Operator on Compact Riemannian Manifolds},
author = {Guofang Wei and Rugang Ye},
journal= {arXiv preprint arXiv:math/0703505},
year = {2007}
}
备注
In Theorem A, the previous maximum estimate in terms of the isoperimetric constant is replaced by a maximum estimate in terms of the volume-normalized isoperimetric constant. The statements of Gallot's estimate for the isoperimetric constant are corrected