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The $ r$-stability of hypersurfaces with zero Gauss-Kronecker curvature


Author: Marcos P. A. Cavalcante
Journal: Proc. Amer. Math. Soc. 136 (2008), 287-294
MSC (2000): Primary 53C42, 53A07; Secondary 35P15
DOI: https://doi.org/10.1090/S0002-9939-07-08941-1
Published electronically: September 24, 2007
MathSciNet review: 2350415
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Abstract: In this paper we give sufficient conditions for a bounded domain in an $ r$-minimal hypersurface of the Euclidean space to be $ r$-stable. The Gauss-Kronecker curvature of this hypersurface may be zero on a set of capacity zero.


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Additional Information

Marcos P. A. Cavalcante
Affiliation: Instituto de Matemática, Universidade Federal de Alagoas, Campus A. C. Simões, BR 104, Norte, Km 97, 57072-970, Maceió, AL, Brazil
Email: petrucio@impa.br

DOI: https://doi.org/10.1090/S0002-9939-07-08941-1
Keywords: $r$-minimal immersions, $r$-stability, capacity.
Received by editor(s): April 20, 2006
Received by editor(s) in revised form: September 22, 2006
Published electronically: September 24, 2007
Additional Notes: The author was fully supported by CNPq-Brazil.
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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