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ON ALMOST STABLE CMC HYPERSURFACES IN MANIFOLDS OF BOUNDED SECTIONAL CURVATURE

Part of: Global differential geometry

Published online by Cambridge University Press:  10 September 2019

JULIEN ROTH Open the ORCID record for JULIEN ROTH [Opens in a new window]  and
ABHITOSH UPADHYAY Open the ORCID record for ABHITOSH UPADHYAY [Opens in a new window]
JULIEN ROTH
Affiliation:
Laboratoire d’Analyse et de Mathématiques Appliquées, UPEM-UPEC, CNRS, F-77454 Marne-la-Vallée, France email julien.roth@u-pem.fr
ABHITOSH UPADHYAY*
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India email abhi.basti.ipu@gmail.com, abhitoshu@iisc.ac.in
*
✉abhi.basti.ipu@gmail.com, abhitoshu@iisc.ac.in
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Abstract

We show that almost stable constant mean curvature hypersurfaces contained in a sufficiently small ball of a manifold of bounded sectional curvature are close to geodesic spheres.

Keywords

stable constant mean curvaturehypersurfacegeodesic sphere

MSC classification

Primary: 53C24: Rigidity results
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 2 , April 2020 , pp. 333 - 338
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

The second author gratefully acknowledges the support of a National Post-doctoral Fellowship (file no. PDF/2017/001165) from the Science and Engineering Research Board, Government of India.

References

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