General estimate of the first eigenvalue on manifolds

Mu-Fa Chen

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arXiv · 1111.6663

General estimate of the first eigenvalue on manifolds

Mu-Fa Chen

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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.

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Mu-Fa Chen. 2011-11-29. General estimate of the first eigenvalue on manifolds. https://arxiv.org/abs/1111.6663

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