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Eigenvalue estimate on complete noncompact Riemannian manifolds and applications |
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| Authors: | Manfredo P. do Carmo Detang Zhou |
| Affiliation: | IMPA, Estrada Dona Castorina, 110-Jardim Botanico 22460-320 Rio de Janeiro, Brazil ; Department of Mathematics, Shandong University, Jinan, Shandong 250100, China |
| 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. |
| Keywords: | Riemannian manifold eigenvalue hypersurface mean curvature |
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