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5. First Eigenvalue, Volume Growth and Ricci Curvature.

Author

Etemad, Azam and Samea, Hojatolah

Subjects
*EIGENVALUES, *CURVATURE, *MANIFOLDS (Mathematics), *RIEMANNIAN manifolds, *DIFFERENTIAL geometry
Abstract

We first prove a new relation between the existence of an upper bound for volume growth in complete Riemannian manifold with the existence of a lower hound for its Ricci curvature. Then we prove that if the Ricci curvature outside the some compact subset of a compelet, non compact Riemannian manifold have an special lower bound then the first eigenvalue for the complement of this subset is zero. [ABSTRACT FROM AUTHOR]

Published
2005

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