DC FieldValueLanguage
dc.contributor.author賴建綸en_US
dc.contributor.authorLai, Chien-Lunen_US
dc.contributor.author許義容en_US
dc.contributor.authorHsu, Yi-Jungen_US
dc.date.accessioned2015-11-26T00:56:03Z-
dc.date.available2015-11-26T00:56:03Z-
dc.date.issued2015en_US
dc.identifier.urihttp://140.113.39.130/cdrfb3/record/nctu/#GT079722807en_US
dc.identifier.urihttp://hdl.handle.net/11536/126169-
dc.description.abstract假設M 是一個體積為無窮之完備黎曼流形, ­是在 M 上的一個緊致集. 分別在體積成長跟Ricci 曲率的下界的條件下, 去估計(M \ Omega ­) 之第一固有值的上界. 研究方法主要是根據二次微分方程解的漸近行為跟max-min principle 及Bishop 比較定理.zh_TW
dc.description.abstractLet 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.en_US
dc.language.isoen_USen_US
dc.subject第一固有值zh_TW
dc.subject完備流形zh_TW
dc.subject上界估計zh_TW
dc.subjectcomplete Riemannian manifoldsen_US
dc.subjectfirst eigenvalueen_US
dc.subjectupper bound estimatesen_US
dc.title完備流形第一固有值之上界估計zh_TW
dc.titleUpper bounds for the first eigenvalue of the Laplace operator on complete Riemannian manifoldsen_US
dc.typeThesisen_US
dc.contributor.department應用數學系所zh_TW
Appears in Collections:Thesis