Upper bounds for the first eigenvalue of the Laplace operator on complete Riemannian manifolds
博士 === 國立交通大學 === 應用數學系所 === 103 === Let M be a complete Riemannian manifold with infnite volume and be a compact subdomain in M. In this thesis we obtain two upper bound estimates for the first eigenvalue of the Laplacian on the punctured manifold M \ Omega subject to volume growth and lower bo...
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| Format: | Others |
| Language: | en_US |
| Published: |
2015
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| Online Access: | http://ndltd.ncl.edu.tw/handle/35566133860064821906 |
| Summary: | 博士 === 國立交通大學 === 應用數學系所 === 103 === Let M be a complete Riemannian manifold with infnite volume and be a compact subdomain in M. In this thesis we obtain two upper bound estimates for the first eigenvalue of the Laplacian on the punctured manifold M \ Omega subject to
volume growth and lower bound of Ricci curvature, respectively. The proof hinges on asymptotic behavior of solutions of second order differential equations, the max-min principle and Bishop volume comparison theorem.
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