Eigenvalue Estimates on Bakry-Emery Manifolds

被引：4

作者：

Charalambous, Nelia ^{[1
]}

Lu, Zhiqin ^{[2
]}

Rowlett, Julie ^{[3
,4
]}

机构：

[1] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

[2] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[3] Chalmers Univ Technol, Math Sci, SE-41296 Gothenburg, Sweden

[4] Univ Gothenburg, SE-41296 Gothenburg, Sweden

来源：

ELLIPTIC AND PARABOLIC EQUATIONS | 2015年 / 119卷

基金：

美国国家科学基金会;

关键词：

SCHRODINGER-OPERATORS; RICCI CURVATURE; 1ST EIGENVALUE; LOWER BOUNDS; LAPLACIAN; KERNEL; DIAMETER; GAP;

D O I：

10.1007/978-3-319-12547-3_2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We demonstrate lower bounds for the eigenvalues of compact Bakry-Emery manifolds with and without boundary. The lower bounds for the first eigenvalue rely on a generalized maximum principle which allows gradient estimates in the Riemannian setting to be directly applied to the Bakry-Emery setting. Lower bounds for all eigenvalues are demonstrated using heat kernel estimates and a suitable Sobolev inequality.

引用

页码：45 / 61

页数：17

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