極小曲面的極小極大構造法

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。

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.