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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李瑩英(Yng-Ing Lee) | |
| dc.contributor.author | Wei-Bo Su | en |
| dc.contributor.author | 蘇瑋栢 | zh_TW |
| dc.date.accessioned | 2021-06-16T05:33:55Z | - |
| dc.date.available | 2014-08-21 | |
| dc.date.copyright | 2014-08-21 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-08-13 | |
| dc.identifier.citation | [Bra78] Kenneth A. Brakke. The motion of a surface by its mean curvature, volume 20 of Mathematical Notes. Princeton University Press, Princeton, N.J., 1978.
[CL04] Jingyi Chen and Jiayu Li. Singularity of mean curvature flow of Lagrangian submanifolds. Invent. Math., 156(1):25–51, 2004. [Gro99] Mark Gross. Special Lagrangian fibrations. II. Geometry. A survey of tech- niques in the study of special Lagrangian fibrations. In Surveys in differential geometry: differential geometry inspired by string theory, volume 5 of Surv. Differ. Geom., pages 341–403. Int. Press, Boston, MA, 1999. [Gro01] Mark Gross. Special Lagrangian fibrations. I. Topology [ MR1672120 (2000e:14066)]. In Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds (Cambridge, MA, 1999), volume 23 of AMS/IP Stud. Adv. Math., pages 65–93. Amer. Math. Soc., Providence, RI, 2001. [Hit97] Nigel J. Hitchin. The moduli space of special Lagrangian submanifolds. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 25(3-4):503–515 (1998), 1997. Dedicated to Ennio De Giorgi. [JLT10] Dominic Joyce, Yng-Ing Lee, and Mao-Pei Tsui. Self-similar solutions and translating solitons for Lagrangian mean curvature flow. J. Differential Geom., 84(1):127–161, 2010. [Joy03a] Dominic Joyce. Singularities of special Lagrangian fibrations and the SYZ conjecture. Comm. Anal. Geom., 11(5):859–907, 2003. [Joy03b] Dominic Joyce. Special Lagrangian submanifolds with isolated conical sin- gularities. V. Survey and applications. J. Differential Geom., 63(2):279–347, 2003. [Joy03c] Dominic Joyce. U(1)-invariant special Lagrangian 3-folds in C3 and special Lagrangian fibrations. Turkish J. Math., 27(1):99–114, 2003. [Law89] Gary Lawlor. The angle criterion. Invent. Math., 95(2):437–446, 1989. [LN14] Jason D. Lotay and Andre Neves. Uniqueness of lagrangian self-expanders. arXiv:1208.2729 [math.DG], 2014. [LW09] Yng-Ing Lee and Mu-Tao Wang. Hamiltonian stationary shrinkers and ex- panders for Lagrangian mean curvature flows. J. Differential Geom., 83(1): 27–42, 2009. [McL98] Robert C. McLean. Deformations of calibrated submanifolds. Comm. Anal. Geom., 6(4):705–747, 1998. [Nev07] Andre Neves. Singularities of Lagrangian mean curvature flow: zero-Maslov class case. Invent. Math., 168(3):449–484, 2007. [Nev11] Andre Neves. Recent progress on singularities of Lagrangian mean curvature flow. In Surveys in geometric analysis and relativity, volume 20 of Adv. Lect. Math. (ALM), pages 413–438. Int. Press, Somerville, MA, 2011. [Nev13] Andre Neves. Finite time singularities for Lagrangian mean curvature flow. Ann. of Math. (2), 177(3):1029–1076, 2013. [Sei00] Paul Seidel. Graded Lagrangian submanifolds. Bull. Soc. Math. France, 128(1):103–149, 2000. [Smo] Knut Smoczyk. A canonical way to deform a lagrangian submanifold. arXiv:dg-ga/9605005. [Smo02] Knut Smoczyk. Angle theorems for the Lagrangian mean curvature flow. Math. Z., 240(4):849–883, 2002. [SW02] Knut Smoczyk and Mu-Tao Wang. Mean curvature flows of Lagrangians sub- manifolds with convex potentials. J. Differential Geom., 62(2):243–257, 2002. [SYZ01] Andrew Strominger, Shing-Tung Yau, and Eric Zaslow. Mirror symmetry is T -duality [ MR1429831 (97j:32022)]. In Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds (Cambridge, MA, 1999), vol- ume 23 of AMS/IP Stud. Adv. Math., pages 333–347. Amer. Math. Soc., Prov- idence, RI, 2001. [Tho01] R. P. Thomas. Moment maps, monodromy and mirror manifolds. In Symplec- tic geometry and mirror symmetry (Seoul, 2000), pages 467–498. World Sci. Publ., River Edge, NJ, 2001. [TY02] R. P. Thomas and S.-T. Yau. Special Lagrangians, stable bundles and mean curvature flow. Comm. Anal. Geom., 10(5):1075–1113, 2002. [UY86] K. Uhlenbeck and S.-T. Yau. On the existence of Hermitian-Yang-Mills connections in stable vector bundles. Comm. Pure Appl. Math., 39(S, suppl.):S257–S293, 1986. Frontiers of the mathematical sciences: 1985 (New York, 1985). [Wan01a] Mu-Tao Wang. Deforming area preserving diffeomorphism of surfaces by mean curvature flow. Math. Res. Lett., 8(5-6):651–661, 2001. [Wan01b] Mu-Tao Wang. Mean curvature flow of surfaces in Einstein four-manifolds. J. Differential Geom., 57(2):301–338, 2001. [Wan08a] Mu-Tao Wang. A convergence result of the Lagrangian mean curvature flow. In Third International Congress of Chinese Mathematicians. Part 1, 2, vol- ume 2 of AMS/IP Stud. Adv. Math., 42, pt. 1, pages 291–295. Amer. Math. Soc., Providence, RI, 2008. [Wan08b] Mu-Tao Wang. Some recent developments in Lagrangian mean curvature flows. In Surveys in differential geometry. Vol. XII. Geometric flows, vol- ume 12 of Surv. Differ. Geom., pages 333–347. Int. Press, Somerville, MA, 2008. [Yau78] Shing Tung Yau. On the Ricci curvature of a compact Kahler manifold and the complex Monge-Ampere equation. I. Comm. Pure Appl. Math., 31(3):339– 411, 1978. [YI14] Joana Oliveira dos Santos Yohsuke Imagi, Dominic Joyce. Uniqueness results for special lagrangians and lagrangian mean curvature flow expanders in cm. arXiv:1404.0271 [math.SG], 2014. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/56542 | - |
| dc.description.abstract | 第一部分把拉格朗日子流形的幾何和一些已知的結果做一個大略的 簡介,文中特別討論了 Hitchin 對於特殊拉格朗日子流形的模空間結構 的研究結果。
第二部分開始利用均曲率流來研究特殊拉格朗日子流形在卡拉 比 -丘空間中的存在性。除了簡介一些已知結果外,我們會在文中仔 細討論由 Joyce-Lee-Tsui 所給出的自相似解。最後我們會簡介一個由 Thomas-Yau 給出的一個關於特殊拉格朗日子流形存在性的猜想。 | zh_TW |
| dc.description.abstract | In the first part of this thesis, we survey and summarize some known re- sults in Lagrangian and special Lagrangian geometry. In particular we fo- cus on the structure of the moduli space of special Lagrangian subamanifolds studied by Hitchin.
In the second part, we focus on the theory of Lagrangian mean curvature flow, especially the Lagrangian self-similar solutions constructed by Joyce- Lee-Tsui. At the end we describe an unsolved conjecture given by Thomas and Yau. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T05:33:55Z (GMT). No. of bitstreams: 1 ntu-103-R01221006-1.pdf: 949751 bytes, checksum: 6aebbe0f7a192204ac9ac4b5061e889c (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 口試委員會審定書 i
致謝 ii 中文摘要 iii Abstract iv Contents iv 1 Introduction 1 2 Preliminaries 3 2.1 Calabi-YauManifolds............................ 3 2.2 Lagrangian Submanifolds.......................... 4 2.3 Special Lagrangian Submanifolds ..................... 8 3 Moduli Space of Special Lagrangian Submanifolds 12 3.1 Deformations of Special Lagrangian Submanifolds . . . . . . . . . . . . 12 3.2 Local Coordinates on the Moduli Space M ................ 13 3.3 Lagranigan structure on M ......................... 16 3.4 Kahler Structure on the Complexified Moduli Space. . . . . . . . . . . . 18 3.5 The SYZ conjecture............................. 22 4 Lagrangian Mean Curvature Flow 23 4.1 Introduction to Lagrangian Mean Curvature Flow . . . . . . . . . . . . . 23 4.2 Singularities of Lagrangian Mean Curvature Flow . . . . . . . . . . . . . 26 4.3 Self-similar Solutions............................ 29 4.4 The Brakke motion ............................. 31 5 The Joyce-Lee-Tsui Self-similar Solutions 33 5.1 Construction of Self-similar Solutions ................... 33 5.2 Self-expanders ............................... 37 5.3 A Brakke Motion Coming Out From a Lagrangian Cone. . . . . . . . . . . 41 6 The Thomas-Yau Conjecture 44 6.1 The moment map .............................. 44 6.2 Lagrangian Surgeries ............................ 45 6.3 The Thomas-Yau Stability ......................... 46 | |
| dc.language.iso | zh-TW | |
| dc.subject | 均曲率流 | zh_TW |
| dc.subject | 拉格朗日子流形 | zh_TW |
| dc.subject | 特殊拉格朗日子流形 | zh_TW |
| dc.subject | special Lagrangian submanifold | en |
| dc.subject | mean curvature flow | en |
| dc.subject | Lagrangian submanifold | en |
| dc.title | 卡拉比 -丘流形中的拉格朗日和特殊拉格朗日子流形 | zh_TW |
| dc.title | Lagrangian and Special Lagrangian Submanifolds in a Calabi-Yau Manifold | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 崔茂培(Mao-Pei Tsui),蔡忠潤(Chung-Jun Tsai),王慕道(Mu-Tao Wang),陳泊寧(Po-Ning Chen) | |
| dc.subject.keyword | 均曲率流,拉格朗日子流形,特殊拉格朗日子流形, | zh_TW |
| dc.subject.keyword | mean curvature flow,Lagrangian submanifold,special Lagrangian submanifold, | en |
| dc.relation.page | 51 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-08-13 | |
| 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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