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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/57175完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李瑩英 | |
| dc.contributor.author | Yuan Shyong Ooi | en |
| dc.contributor.author | 黃垣熊 | zh_TW |
| dc.date.accessioned | 2021-06-16T06:36:56Z | - |
| dc.date.available | 2014-08-08 | |
| dc.date.copyright | 2014-08-08 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-07-31 | |
| dc.identifier.citation | [All] W.K. Allard, On the first variation of a varifold, Ann.of Math.(2) 95 (1972) no. 3, 417--491.
[Alm] F.J. Almgren, The theory of varifolds, Mimeographed notes, Princeton, 1965. [CD]T.H. Colding and C. De Lellis, The min-max construction of minimal surfaces, Surveys in differential geometry, Vol. 8, Lectures on Geometry and Topology. [CP] C. De Lellis and F. Pellandini, Genus bounds for minimal surfaces arising from min-max constructions, J.Reine Angew. Math. 644(2010), 47--99. [CM] T.H. Colding and W.P. Minicozzi. A course in minimal surfaces. Vol. 121. American Mathematical Soc., (2011). [J]J. Jost, Embedded minimal surfaces in manifolds diffeomorphic to the three-dimensional ball or sphere, J. Differential Geom. 30(1989), no. 2, 555--577. [MSY]W. Meeks III, L. Simon, and S.T. Yau, Embedded minimal surfaces, exotic spheres, and manifolds with positive ricci curvature Ann.of Math.(2) 116 (1982) no. 3, 621--659. [MN] F. C. Marques and A. Neves, Rigidity of min-max minimal spheres in three-manifolds, Duke Mathematical Journal 161 (2012), no. 14,2725-2752. [MN2]F. C. Marques and A. Neves, Min-Max theory and the Willmore conjecture, Annals of Mathematics 179 (2014): 683-782. [MN3]F. C. Marques and A. Neves, Existence of infinitely many minimal hypersurfaces in positive Ricci Curvature, arXiv:1311.6501, (2013) [M]J. W. Milnor, Morse theory (No.51), Princeton university press [P]J.T. Pitts, Existence and regularity of minimal surfaces on Riemannian manifolds. Princeton University Press, Princeton, N.J.;University of Tokyo Press, Tokyo (1981).[PR1]J.T. Pitts and J.H. Rubinstein, Existence of minimal surfaces of bounded topological type in three--manifolds, Miniconference on Geometry and Partial Differential Equations, Proceedings of the Centre for Mathematical Analysis,Australian National University (1985). [PR2]J.T. Pitts and J.H. Rubinstein, Application of minmax to minimal surfaces and the topology of 3-manifolds, Miniconference on Geometry and Partial Differential Equations, Proceedings of the Centre for Mathematical Analysis, Australian National University (1986). [Si]L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University (1983). [Sm]F. Smith, On the existence of embedded minimal 2-spheres in the 3-sphere, endowed with an arbitrary Riemannian metric, supervisor L. Simon, University of Melbourne (1982). [SS]R. Schoen, L.Simon, Regularity of stable minimal hypersurfaces, Comm. Pure Appl. Math. 34(1981), 741--797 [U]F. Urbano, Second variation of one-sided complete minimal surfaces, Rev. Mat. Iberoam. 29(2013), no. 2, 479--494 [MPT]Jose M.Manzano, Julia Plehnert, Francisco Torralbo, Compact embedded minimal surfaces in S^2 x S^1, arXiv:1311.2500, (2013) [XZ]X.Zhou, Min-max minimal hypersurface in (M^{n+ 1}, g) with Ric_g> 0 and 2leq nleq 6, arXiv preprint arXiv:1210.2112 (2012). [XZ2]X.Zhou, On the existence of min-max minimal surface of genus ggeq 2, arXiv preprint arXiv:1111.6206 (2011) | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/57175 | - |
| dc.description.abstract | 本論文將討論如何通過極小極大方法來構造極小曲面。我們主要討論在這方法之下，極小曲面的存在性問題。
這方法有很多不同的版本，我們主要的參考文獻來自 Colding 和 De Lellis 的 The min-max construction of minimal surfaces[CD]。我們也將會在第一章節提到其他造極小曲面的極小極大方法。 | zh_TW |
| dc.description.abstract | In this thesis, we shall survey the construction of minimal surface in closed three-manifold via min-max construction.
Our focus will be on the existence of the min-max stationary varifold via this construction. There are many different type min-max construction. Our main reference is The min-max construction of minimal surfaces [CD] by Colding and De Lellis in which they apply min-max method in the isotopy class of generalized family of surfaces. We shall also mention some other min-max method in the introduction part. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T06:36:56Z (GMT). No. of bitstreams: 1 ntu-103-R00221030-1.pdf: 597520 bytes, checksum: b31fe63e07c7c31062fd734dfc1dc238 (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 致謝 i
中文摘要 ii Abstract iii 1. Introduction 1 2. Preliminaries 4 3. Existence of Stationary Min-max Sequence 8 4. Existence of Almost Minimizing Min-max Sequence 14 5. Specific Case for Min-max Method on S^2 x S^1 22 6. Bibliography 24 | |
| dc.language.iso | en | |
| dc.subject | 極小極大構造法 | zh_TW |
| dc.subject | 極小曲面 | zh_TW |
| dc.subject | min-max construction | en |
| dc.subject | minimal surfaces | en |
| dc.title | 極小曲面的極小極大構造法 | zh_TW |
| dc.title | Min-max construction of minimal surface | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王慕道,崔茂培,陳泊寧,蔡忠潤 | |
| dc.subject.keyword | 極小極大構造法,極小曲面, | zh_TW |
| dc.subject.keyword | min-max construction,minimal surfaces, | en |
| dc.relation.page | 26 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-08-01 | |
| 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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