極小流形在反德西特空間的積空間之幾何研究

Abstract

這篇論文主要在理解極小流形靠近邊界的行為，此極小流形是在AdS積空間底下的子流形且在特殊的座標選取下可表示成函數圖形的樣子。從一個特例出發，我們嘗試了解Graham和Karch得出的結果。次外，從Han-Chih Chang的數值圖形可觀察到U形膜有一個極值點，我們證明了確實只有一個極值點。

This thesis focuses on understanding the behavior of a minimal submanifold near boundary where such a minimal submanifold, Z, is in a product space of AdS with a particular coordinate patch such that Z can be described in a special graphic form. Begin from a particular example, we try to know the result derived from Graham and Karch. Besides, there is a critical point in U-shaped brane according to the numerical graph from Han-Chih Chang. We prove that there is only one critical point.