The $r$-stability of hypersurfaces with zero Gauss-Kronecker curvature
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- by Marcos P. A. Cavalcante PDF
- Proc. Amer. Math. Soc. 136 (2008), 287-294 Request permission
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.References
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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
- MR Author ID: 813473
- Email: petrucio@impa.br
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2350415