Foliations of Hyperbolic Space by Constant Mean Curvature Hypersurfaces

被引：3

作者：

Coskunuzer, Baris ^{[1
]}

机构：

[1] Koc Univ, Dept Math Sariyer, TR-34450 Istanbul, Turkey

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2010年 / 2010卷 / 08期

关键词：

STRONG MAXIMUM PRINCIPLE; ASYMPTOTIC BOUNDARY; REGULARITY; EXISTENCE;

D O I：

10.1093/imrn/rnp175

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the constant mean curvature hypersurfaces in Hn+1 spanning the boundary of a star-shaped C-1,C-1 domain in S-infinity(n)(Hn+1) give a foliation of Hn+1. We also show that if Gamma is a closed codimension-1 C-2,C-alpha submanifold in S-infinity(n)(Hn+1) bounding a unique constant mean curvature hypersurface Sigma(H) in Hn+1 with partial derivative(infinity)Sigma(H) = Gamma for any H is an element of (-1,1), then the constant mean curvature hypersurfaces {Sigma(H)} foliate Hn+1.

引用

页码：1417 / 1431

页数：15

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