曲率对调和函数与特征函数凸性性质的影响
偏微分方程分析
2014-01-14 v3 微分几何
谱理论
摘要
本文给出了 Laplace-Beltrami 特征函数的 Donnelly-Fefferman 增长界的一个证明，这可能是最简单且最初等的证明。我们的证明还给出了以曲率界表示的新的定量几何估计，这些估计改进并简化了 Garofalo 和 Lin 先前的工作。该证明基于弯曲流形上调和函数的凸性性质，推广了 Agmon 关于 中调和函数凸性性质的定理。
引用
@article{arxiv.1112.4352,
title = {The effect of curvature on convexity properties of harmonic functions and eigenfunctions},
author = {Dan Mangoubi},
journal= {arXiv preprint arXiv:1112.4352},
year = {2014}
}
备注
24 pages. This is a major revision. The main theorem now treats the case of pinched curvature between any two real values. The proof is simplified in several points. Ricci curvature is replaced by sectional curvature. Referee's remarks incorporated