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ON ALMOST STABLE CMC HYPERSURFACES IN MANIFOLDS OF BOUNDED SECTIONAL CURVATURE

Published online by Cambridge University Press:  10 September 2019

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

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.

Type
Research Article
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.

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