Lower bound estimates for the first eigenvalue of the weighted p-Laplacian on smooth metric measure spaces

被引：31

作者：

Wang, Yu-Zhao ^{[1
]}

Li, Huai-Qian ^{[2
,3
]}

机构：

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

[2] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

[3] Macquarie Univ, Dept Math, N Ryde, NSW 2109, Australia

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2016年 / 45卷

基金：

澳大利亚研究理事会; 中国国家自然科学基金;

关键词：

Eigenvalue estimate; Bakry-Emery Ricci curvature; Smooth metric measure space; Weighted p-Bochner formula; Weighted p-Laplacian; Weighted p-Reilly formula; EQUATIONS; FORMULA; MANIFOLDS; DIAMETER; THEOREMS; OPERATOR; GAP;

D O I：

10.1016/j.difgeo.2015.11.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

New lower bounds of the first nonzero eigenvalue of the weighted p-Laplacian are established on compact smooth metric measure spaces with or without boundaries. Under the assumption of positive lower bound for the m-Bakry Emery Ricci curvature, the Escobar-Lichnerowicz-Reilly type estimates are proved; under the assumption of nonnegative infinity-Bakry Emery Ricci curvature and the m-Bakry-Emery Ricci curvature bounded from below by a non-positive constant, the Li Yau type lower bound estimates are given. The weighted p-Bochner formula and the weighted p-Reilly formula are derived as the key tools for the establishment of the above results. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：23 / 42

页数：20