General estimate of the first eigenvalue on manifolds

Abstract

Ten sharp lower estimates of the first non-trivial eigenvalue of Laplacian on compact Riemannian manifolds are reviewed and compared. An improved variational formula, a general common estimate, and a new sharp one are added. The best lower estimates are now updated. The new estimates provide a global picture of what one can expect by our approach.

Keywords

First non-trivial eigenvalue / sharp estimate / Riemannian manifold

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