極小流形在反德西特空間的積空間之幾何研究

Tzu-Mo Kuo; 郭子模

請用此 Handle URI 來引用此文件： http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/66941

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DC 欄位	值	語言
dc.contributor.advisor	崔茂培
dc.contributor.author	Tzu-Mo Kuo	en
dc.contributor.author	郭子模	zh_TW
dc.date.accessioned	2021-06-17T01:15:20Z	-
dc.date.available	2017-08-25
dc.date.copyright	2017-08-25
dc.date.issued	2017
dc.date.submitted	2017-08-14
dc.identifier.citation	[1] H. C. Chang. Minimal submanifolds asymptotic to AdS4 S2 in AdS5×S5. 1310.5734 [hep-th]. [2] T. H. Colding and W. P. Minicozzi. A course in minimal surfaces. American Mathematical Soc., 2011. [3] L. C. Evans. Partial di erential equations. American Mathematical Soc., 2010. [4] C. R. Graham and A. Karch. Minimal area submanifolds in AdS×compact. hep-th/1401.7692. [5] C. R. Graham and J. Lee. Einstein metrics with prescribed conformal in nity on the ball. Adv. Math. 87(1991), 186-225. [6] J. Maldacena. Wilson loops in large N eld theories. hep-th/9803002. [7] J. Simons. Minimal subvariety in riemannian manifolds. Annals of Mathematics Second Series, Vol. 88, No. 1 (Jul., 1968), pp. 62-105.
dc.identifier.uri	http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/66941	-
dc.description.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。	zh_TW
dc.description.abstract	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.	en
dc.description.provenance	Made available in DSpace on 2021-06-17T01:15:20Z (GMT). No. of bitstreams: 1 ntu-106-R04221014-1.pdf: 964641 bytes, checksum: 1d6035fe21b90482f61b9fbfeaf0548f (MD5) Previous issue date: 2017	en
dc.description.tableofcontents	口試委員會審定書.................................................# 誌謝.............................................................i 中文摘要........................................................ii ABSTRACT.......................................................iii CONTENTS........................................................iv Chapter 1 Introduction.....................................1 Chapter 2 Preliminary......................................3 2.1 Notation...........................................3 2.2 The first and second variation formulas............3 2.3 Linearization of mean curvature vector.............4 2.4 Conformal compact Einstein manifold................5 Chapter 3 Behavior of Product Submanifold Near Boundary....8 Chapter 4 Examples of Graphical Minimal Submanifold.......13 4.1 Minimal submanifold in AdS_5×S^5..................13 4.2 U-shaped brane....................................15 Bibliography....................................................17
dc.language.iso	en
dc.subject	AdS	zh_TW
dc.subject	極小流形	zh_TW
dc.subject	U形膜	zh_TW
dc.subject	極值點	zh_TW
dc.subject	critical point	en
dc.subject	AdS	en
dc.subject	U-shaped brane	en
dc.subject	minimal submanifold	en
dc.title	極小流形在反德西特空間的積空間之幾何研究	zh_TW
dc.title	Survey on the Geometry of Minimal Submanifold in Product Space of Anti-de Sitter Space	en
dc.type	Thesis
dc.date.schoolyear	105-2
dc.description.degree	碩士
dc.contributor.oralexamcommittee	張樹城,王業凱,蔡忠潤
dc.subject.keyword	極小流形,AdS,U形膜,極值點,	zh_TW
dc.subject.keyword	minimal submanifold,AdS,U-shaped brane,critical point,	en
dc.relation.page	17
dc.identifier.doi	10.6342/NTU201703119
dc.rights.note	有償授權
dc.date.accepted	2017-08-15
dc.contributor.author-college	理學院	zh_TW
dc.contributor.author-dept	數學研究所	zh_TW
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