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 › peer-review

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

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

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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.",

keywords = "Constant mean curvature, Hyperbolic space, Nonparabolic end, Parabolic end, Stable hypersurface",

author = "Chen, {Jui Tang Ray}",

note = "Funding Information: Acknowledgements The author would like to thank Professor J. Wang and Professor S.C. Chang for their interest in this work. Research supported in part by NSC of Taiwan.",

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language = "English",

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N1 - Funding Information: Acknowledgements The author would like to thank Professor J. Wang and Professor S.C. Chang for their interest in this work. Research supported in part by NSC of Taiwan.

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N2 - 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.

AB - 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.

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KW - Nonparabolic end

KW - Parabolic end

KW - Stable hypersurface

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