指導教授：李瑩英臺灣大學：數學研究所蘇瑋栢Su, Wei-BoWei-BoSu2014-11-302018-06-282014-11-302018-06-282014http://ntur.lib.ntu.edu.tw//handle/246246/264015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。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.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 ......................... 46949751 bytesapplication/pdf論文公開時間：2014/08/21論文使用權限：同意有償授權(權利金給回饋學校)均曲率流拉格朗日子流形特殊拉格朗日子流形thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/264015/1/ntu-103-R01221006-1.pdf