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Transactions of the American Mathematical Society

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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
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.

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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@

Detang Zhou
Affiliation: Department of Mathematics, Shandong University, Jinan, Shandong 250100, China

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