Stable complete noncompact hypersurfaces with constant mean curvature

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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 languageEnglish
Pages (from-to)161-190
Number of pages30
JournalAnnals of Global Analysis and Geometry
Volume36
Issue number2
DOIs
Publication statusPublished - 2009 Jul 1

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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