Eigenvalue estimate on complete noncompact Riemannian manifolds and applications

do Carmo, Manfredo; Zhou, Detang

doi:10.1090/S0002-9947-99-02061-9

Eigenvalue estimate on complete noncompact Riemannian manifolds and applications
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by Manfredo P. do Carmo and Detang Zhou PDF

Trans. Amer. Math. Soc. 351 (1999), 1391-1401 Request permission

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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