The Spectrum of the Martin-Morales-Nadirashvili Minimal Surfaces Is Discrete

被引：7

作者：

Bessa, G. Pacelli ^{[1
]}

Jorge, Luquesio P. ^{[1
]}

Montenegro, J. Fabio ^{[1
]}

机构：

[1] Univ Fed Ceara, Dept Math, BR-60455760 Fortaleza, Ceara, Brazil

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2010年 / 20卷 / 01期

关键词：

Proper bounded minimal submanifolds; Discrete spectrum; Essential spectrum; PURELY CONTINUOUS-SPECTRUM; RIEMANNIAN-MANIFOLDS; NEGATIVE CURVATURE;

D O I：

10.1007/s12220-009-9101-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the spectrum of a complete submanifold properly immersed into a ball of a Riemannian manifold is discrete, provided the norm of the mean curvature vector is sufficiently small. In particular, the spectrum of a complete minimal surface properly immersed into a ball of R(3) is discrete. This gives a positive answer to a question of Yau (Asian J. Math. 4: 235-278, 2000).

引用

页码：63 / 71

页数：9

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