First stability eigenvalue characterization of Clifford hypersurfaces
Author:
Oscar Perdomo
Journal:
Proc. Amer. Math. Soc. 130 (2002), 33793384
MSC (2000):
Primary 53A10
Published electronically:
April 11, 2002
MathSciNet review:
1913017
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Abstract: The stability operator of a compact oriented minimal hypersurface is given by , where is the norm of the second fundamental form. Let be the first eigenvalue of and define . In 1968 Simons proved that for any nonequatorial minimal hypersurface . In this paper we will show that only for Clifford hypersurfaces. For minimal surfaces in , let denote the area of and let denote the genus of . We will prove that . Moreover, if is embedded, then we will prove that . If in addition to the embeddeness condition we have that , then we will prove that .
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Additional Information
Oscar Perdomo
Affiliation:
Departamento de Matematicas, Universidad del Valle, Cali, Colombia
Email:
osperdom@mafalda.univalle.edu.co
DOI:
http://dx.doi.org/10.1090/S0002993902064511
PII:
S 00029939(02)064511
Received by editor(s):
September 8, 2000
Received by editor(s) in revised form:
June 6, 2001
Published electronically:
April 11, 2002
Communicated by:
Bennett Chow
Article copyright:
© Copyright 2002
American Mathematical Society
