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General estimate of the first eigenvalue on manifolds

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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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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education, Beijing, 100875, China

    Mu-Fa Chen

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  1. Mu-Fa Chen
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Chen, MF. General estimate of the first eigenvalue on manifolds. Front. Math. China 6, 1025–1043 (2011). https://doi.org/10.1007/s11464-011-0164-3

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  • DOI: https://doi.org/10.1007/s11464-011-0164-3

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