Stability properties for the higher dimensional catenoid in

Authors:
Luen-fai Tam and Detang Zhou

Journal:
Proc. Amer. Math. Soc. **137** (2009), 3451-3461

MSC (2000):
Primary 53A10; Secondary 53C42

DOI:
https://doi.org/10.1090/S0002-9939-09-09962-6

Published electronically:
May 7, 2009

MathSciNet review:
2515414

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Abstract: This paper concerns some stability properties of higher dimensional catenoids in with . We prove that higher dimensional catenoids have index one. We use -stablity for minimal hypersurfaces and show that the catenoid is -stable and that a complete -stable minimal hypersurface is a catenoid or a hyperplane provided the second fundamental form satisfies some decay conditions.

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Additional Information

**Luen-fai Tam**

Affiliation:
The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, People’s Republic of China

Email:
lftam@math.cuhk.edu.hk

**Detang Zhou**

Affiliation:
Instituto de Matematica, Universidade Federal Fluminense, Centro, Niterói, RJ 24020-140, Brazil

Email:
zhou@impa.br

DOI:
https://doi.org/10.1090/S0002-9939-09-09962-6

Keywords:
Catenoid,
minimal hypersurface,
stability.

Received by editor(s):
January 26, 2009

Published electronically:
May 7, 2009

Additional Notes:
The first author’s research was partially supported by Earmarked Grant of Hong Kong #CUHK403005

The second author’s research was supported by CNPq and FAPERJ of Brazil.

Communicated by:
Chuu-Lian Terng

Article copyright:
© Copyright 2009
American Mathematical Society