Eigenvalue estimate on complete noncompact Riemannian manifolds and applications

Authors:
Manfredo P. do Carmo and Detang Zhou

Journal:
Trans. Amer. Math. Soc. **351** (1999), 1391-1401

MSC (1991):
Primary 53C42; Secondary 53A10, 53C20, 35J60

DOI:
https://doi.org/10.1090/S0002-9947-99-02061-9

MathSciNet review:
1451597

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Abstract | References | Similar Articles | Additional Information

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.

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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:
https://doi.org/10.1090/S0002-9947-99-02061-9

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

Article copyright:
© Copyright 1999
American Mathematical Society