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.
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页码：45 / 61
页数：17
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