指導教授：李瑩英臺灣大學：數學研究所黃垣熊Ooi, Yuan ShyongYuan ShyongOoi2014-11-302018-06-282014-11-302018-06-282014http://ntur.lib.ntu.edu.tw//handle/246246/264034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。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.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 24597520 bytesapplication/pdf論文公開時間：2014/08/08論文使用權限：同意有償授權(權利金給回饋學校)極小極大構造法極小曲面thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/264034/1/ntu-103-R00221030-1.pdf