Stable complete noncompact hypersurfaces with constant mean curvature

Jui Tang Ray Chen

doi:10.1007/s10455-009-9155-y

Stable complete noncompact hypersurfaces with constant mean curvature

Jui Tang Ray Chen

Department of Mathematics

Research output: Contribution to journal › Article

2 Citations (Scopus)

Abstract

This article concerns the structure of complete noncompact stable hypersurfaces Mⁿ with constant mean curvature H > 0 in a complete noncompact oriented Riemannian manifold Nⁿ⁺¹. In particular, we show that a complete noncompact stable constant mean curvature hypersurface Mⁿ, n = 5, 6, in the Euclidean space must have only one end. Any such hypersurface in the hyperbolic space with, respectively, has only one end.

Original language	English
Pages (from-to)	161-190
Number of pages	30
Journal	Annals of Global Analysis and Geometry
Volume	36
Issue number	2
DOIs	https://doi.org/10.1007/s10455-009-9155-y
Publication status	Published - 2009 Jul 1

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Keywords

Constant mean curvature
Hyperbolic space
Nonparabolic end
Parabolic end
Stable hypersurface

ASJC Scopus subject areas

Analysis
Political Science and International Relations
Geometry and Topology

Cite this

Chen, J. T. R. (2009). Stable complete noncompact hypersurfaces with constant mean curvature. Annals of Global Analysis and Geometry, 36(2), 161-190. https://doi.org/10.1007/s10455-009-9155-y

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Access to Document

10.1007/s10455-009-9155-y