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The  -stability of hypersurfaces with zero Gauss-Kronecker curvature
Author(s):
Marcos
P. A.
Cavalcante
Journal:
Proc. Amer. Math. Soc.
136
(2008),
287-294.
MSC (2000):
Primary 53C42, 53A07;
Secondary 35P15
Posted:
September 24, 2007
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Abstract:
In this paper we give sufficient conditions for a bounded domain in an  -minimal hypersurface of the Euclidean space to be  -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:
10.1090/S0002-9939-07-08941-1
PII:
S 0002-9939(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
Posted:
September 24, 2007
Additional Notes:
The author was fully supported by CNPq-Brazil.
Communicated by:
Richard A. Wentworth
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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