General estimate of the first eigenvalue on manifolds
Received date: 13 Jan 2011
Accepted date: 02 Nov 2011
Published date: 01 Dec 2011
Copyright
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.
Mu-Fa CHEN . General estimate of the first eigenvalue on manifolds[J]. Frontiers of Mathematics in China, 0 , 6(6) : 1025 -1043 . DOI: 10.1007/s11464-011-0164-3
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