ON THE DISCRETENESS OF THE SPECTRUM OF THE LAPLACIAN ON NONCOMPACT RIEMANNIAN MANIFOLDS

被引：0

作者：

Cianchi, Andrea ^{[1
]}

Maz'ya, Vladimir ^{[2
,3
]}

机构：

[1] Univ Florence, Dipartimento Matemat U Dini, I-50122 Florence, Italy

[2] Univ Liverpool, Dept Math Sci, Liverpool L69 3BX, Merseyside, England

[3] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2011年 / 87卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

ISOPERIMETRIC COMPARISON THEOREM; CURVATURE; SURFACES; CONSTANTS; PROFILES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Necessary and sufficient conditions for the discreteness of the Laplacian on a noncompact Riemannian manifold M are established in terms of the isocapacitary function of M. The relevant capacity takes a different form according to whether M has finite or infinite volume. Conditions involving the more standard isoperimetric function of M can also be derived, but they are only sufficient in general, as we demonstrate by concrete examples.

引用

页码：469 / 491

页数：23

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