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Advances in Geometry

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Minimal hypersurfaces in ℝn × Sm

Jimmy Petean / Juan Miguel Ruiz
Published Online: 2018-03-20 | DOI: https://doi.org/10.1515/advgeom-2017-0060

Abstract

We classify minimal hypersurfaces in ℝn × Sm with n, m ≥ 2 which are invariant by the canonical action of O(n) × O(m). We also construct compact and noncompact examples of invariant hypersurfaces of constant mean curvature. We show that the minimal hypersurfaces and the noncompact constant mean curvature hypersurfaces are all unstable.

Keywords: Minimal hypersurface

MSC 2010: 53C42

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About the article


Received: 2015-02-21

Revised: 2016-06-09

Published Online: 2018-03-20


Funding: The authors are supported by grant 220074 of Fondo Sectorial de Investigación para la Educación SEP-CONACYT.


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0060.

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