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arXiv:1111.6663 [math.PR]AbstractReferencesReviewsResources

General estimate of the first eigenvalue on manifolds

Mu-Fa Chen

Published 2011-11-29Version 1

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.

Comments: 19 pages
Journal: Front. Math. China 2011, 6(6): 1025-1043
Categories: math.PR, math.DG, math.SP
Subjects: 58C40, 35P15
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