請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/18101完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李瑩英 | |
| dc.contributor.author | Yu-Chin Sun | en |
| dc.contributor.author | 孫有慶 | zh_TW |
| dc.date.accessioned | 2021-06-08T00:51:11Z | - |
| dc.date.copyright | 2015-07-20 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-07-01 | |
| dc.identifier.citation | [1]
Fernando C. Marques and Andre Neves, Min-max theory and the Willmore conjecture , Ann. of Math(2) 179 (2014), no. 2, 683782. [2] T. J. Willmore, Note on embedded surfaces, An. Sti. Univ.Al. I. Cuza' Iasi Sect. I a Mat. (N.S.) 11B (1965) 493{496. [3] J. Pitts, Existence and regularity of minimal surfaces on Riemannian manifolds, Mathematical Notes 27, Princeton University Press, Princeton, (1981) [4] R. Kusner, Comparison surfaces for the Willmore problem , Pacifc J. Math. 138 (1989), no. 2, 317345. [5] H. B. Lawson, Complete minimal surfaces in S 3 , Ann. of Math. (2) 92 1970 335374. [6] L. Hsu, R. Kusner and J. Sullivan, Minimizing the squared mean curvature integral for surfaces in space forms , Experiment. Math. 1 (1992), no. 3, 191207. [7] K. A. Brakke, The Surface Evolver , Experiment. Math. 1 (1992), no. 2, 141165. [8] F. Urbano, Minimal surfaces with low index in the three-dimensional sphere , Proc. Amer. Math. Soc. 108 (1990), no. 4, 989992. [9] S. S. Chern, M. DoCarmo, and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length , Proc. Conf. for M. Stone, Univ. Chicago, 1968 [10] J. Simons, Minimal Varieties in Riemannian manifolds , Ann. of Math, 1968 [11] A. Ros, The Willmore conjecture in the real projective space, Math. Res. Lett, 1999. [12] P. Li and S-T. Yau, A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces, Invent. Math. 69 (1982), 269{291. [13] W. Meeks and S-T. Yau, The existence of embedded minimal surfaces and the problem of uniqueness , Math. Z (1982) [14] M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere , J. Math. Soc. Japan (1962) [15] S. Montiel and A. Ros, Minimal immersions of surfaces by the first eigenfunc- tions and conformal area, Invent. Math. 83 (1985), 153{166. [16] Almgren the homotopy groups of the integral cycle groups Topology 1 (1962) 257299. [17] Luis J. Alias, Aldir Brasil Jr. and Oscar Perdomo On the stability index of hypersurfaces with constant mean curvature in spheres Proc. Amer. Math. Soc. 135 (2007), no. 11, 36853693. [18] Lawrence C. Evans, Partial differential equation textbook, American Mathe- matical Society | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/18101 | - |
| dc.description.abstract | 本論文主要內容為探討Fernando C.Marques和Andre Neves所著的論文：Min-max theory and Willmore conjecture(威爾莫猜想)，此論文成功地證明了一九六五年由Tomas Willmore所提出著名的猜想。他們使用了幾何測度論的方法並且應用八零年代由Almgern 和John Pitts所提出Min-max theory給出了證明，此證明整合了許多八零年代的重要結果，例如保角幾何學的種種應用。威爾莫猜想證明其中的關鍵步驟為Urbano的定理，本論文第三章將著重於此，也附上作者欲推廣此定理的一些計算，此外也會將一些Willmore猜想相關的問題討論附上。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2021-06-08T00:51:11Z (GMT). No. of bitstreams: 1 ntu-104-R02221002-1.pdf: 2116630 bytes, checksum: 01a86b17c3336430c8c160865e5e3333 (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | Introduction-1
Background Materials-4 Urbano's Theorem-11 Willmore Conjecture-17 Beyond Willmore Conjecture-21 | |
| dc.language.iso | en | |
| dc.title | 威爾莫猜想及其相關問題之探討 | zh_TW |
| dc.title | A Survey On Willmore Conjecture And Related Problems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 103-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 張樹城,崔茂培 | |
| dc.subject.keyword | 威爾莫猜想,厄爾巴諾定理, | zh_TW |
| dc.subject.keyword | willmore conjecture, | en |
| dc.relation.page | 27 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2015-07-01 | |
| 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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