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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李瑩英 | |
| dc.contributor.author | Kai-Wei Zhao | en |
| dc.contributor.author | 趙凱衞 | zh_TW |
| dc.date.accessioned | 2021-05-15T17:51:47Z | - |
| dc.date.available | 2014-08-21 | |
| dc.date.available | 2021-05-15T17:51:47Z | - |
| dc.date.copyright | 2014-08-21 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-08-14 | |
| dc.identifier.citation | [BGM] M. Berger, P. Gauduchon and E. Mazet, Le spectre d’une variete riemannienne, Lecture Notes in Mathematics, Vol. 194, Springer, Berlin, 1971.
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/5090 | - |
| dc.description.abstract | 本論文將統整一些在球面、投影實平面以及輪胎面上求得以面積表示的拉普拉斯算子第一特徵值最優上界之方法。 | zh_TW |
| dc.description.abstract | In this thesis, we will summarize some approaches to obtain sharp upper bounds of the first nonzero eigenvalues of the Laplacian operators on closed surfaces, including sphere S2, real projective plane RP2 and torus T2, in terms of their areas. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-15T17:51:47Z (GMT). No. of bitstreams: 1 ntu-103-R01221005-1.pdf: 714680 bytes, checksum: cb04573f369534fffb98fd5b81f0c159 (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 口試委員審定書i
致謝ii 中文摘要iii Abstract iv 1 Introduction 1 2 Sharp upper bound on S2 7 2.1 Conformal automorphisms on sphere 7 2.2 Hersch’s theorem 16 3 Sharp upper bound on RP2 19 3.1 Minimal immersions into sphere 19 3.2 Conformal area 24 3.3 λ1-minimal surfaces 31 4 Sharp upper bound on T2 37 4.1 Variational method on eigenvalue problem 37 4.2 The structure of extremal metrics of eigenvalue functionals 42 4.3 Sharp upper bound of the first eigenvalue on torus 47 5 Open problems 49 References 50 | |
| dc.language.iso | en | |
| dc.title | 封閉曲面上拉普拉斯算子第一特徵值的最優上界 | zh_TW |
| dc.title | Sharp Upper Bounds of the First Eigenvalues of the Laplacian
Operators on Closed Surfaces | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 崔茂培,王慕道,陳泊寧,蔡忠潤 | |
| dc.subject.keyword | 拉普拉斯算子,特徵值問題,譜幾何,最優上界,最優不等式, | zh_TW |
| dc.subject.keyword | Laplacian operator,eigenvalue problem,spectrum geometry,sharp upper bound,sharp inequality, | en |
| dc.relation.page | 52 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2014-08-14 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-103-1.pdf | 697.93 kB | Adobe PDF | 檢視/開啟 |
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