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Eigenvalue estimate on complete noncompact Riemannian manifolds and applications
Author(s):
Manfredo
P.
do Carmo;
Detang
Zhou
Journal:
Trans. Amer. Math. Soc.
351
(1999),
1391-1401.
MSC (1991):
Primary 53C42;
Secondary 53A10, 53C20, 35J60
MathSciNet review:
1451597
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Abstract:
We obtain some sharp estimates on the first eigenvalues of complete noncompact Riemannian manifolds under assumptions of volume growth. Using these estimates we study hypersurfaces with constant mean curvature and give some estimates on the mean curvatures.
References:
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Additional Information:
Manfredo
P.
do Carmo
Affiliation:
IMPA, Estrada Dona Castorina, 110-Jardim Botanico 22460-320 Rio de Janeiro, Brazil
Email:
manfredo@ impa.br
Detang
Zhou
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong 250100, China
DOI:
10.1090/S0002-9947-99-02061-9
PII:
S 0002-9947(99)02061-9
Keywords:
Riemannian manifold,
eigenvalue,
hypersurface,
mean curvature
Received by editor(s):
November 15, 1996
Received by editor(s) in revised form:
February 28, 1997
Additional Notes:
Supported partially by NNSFC and TWAS-IMPA membership
Copyright of article:
Copyright
1999,
American Mathematical Society
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