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On the geometry of conformally compa...

Wang, Xiaodong.

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On the geometry of conformally compact Einstein manifolds.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	On the geometry of conformally compact Einstein manifolds./
作者:	Wang, Xiaodong.
面頁冊數:	81 p.
附註:	Adviser: Richard Schoen.
Contained By:	Dissertation Abstracts International62-09B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3026929
ISBN:	9780493383675

On the geometry of conformally compact Einstein manifolds.
Wang, Xiaodong.

On the geometry of conformally compact Einstein manifolds. - 81 p.

Adviser: Richard Schoen.

Thesis (Ph.D.)--Stanford University, 2001.

This thesis is divided into two parts. The first part studies conformally compact Einstein manifolds. We first give a brief history of the subject, including the recent work of Witten-Yau and Cai-Galloway. Based on their methods a new simple proof of Lee's theorem concerning the spectrum is given. By studying L2 harmonic forms an optimal homology vanishing theorem is established which generalizes the theorem of Witten-Yau and Cai-Galloway. We also study the relationship between Killing vector fields and conformal vector fields on the conformal infinity. A uniqueness theorem is proved under curvature pinching conditions for a conformally compact Einstein manifold whose conformal infinity is conformally flat. Interesting examples are discussed and a nonexistence theorem is proved using Killing spinors. In the second part we define mass for a manifold which is asymptotic to the hyperbolic space in a certain sense and prove the corresponding positive mass theorem using Killing spinors assuming the positive energy condition. At the end a Penrose-type conjecture is discussed.

ISBN: 9780493383675Subjects--Topical Terms:

515831
Mathematics.

On the geometry of conformally compact Einstein manifolds.
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520 $a This thesis is divided into two parts. The first part studies conformally compact Einstein manifolds. We first give a brief history of the subject, including the recent work of Witten-Yau and Cai-Galloway. Based on their methods a new simple proof of Lee's theorem concerning the spectrum is given. By studying L2 harmonic forms an optimal homology vanishing theorem is established which generalizes the theorem of Witten-Yau and Cai-Galloway. We also study the relationship between Killing vector fields and conformal vector fields on the conformal infinity. A uniqueness theorem is proved under curvature pinching conditions for a conformally compact Einstein manifold whose conformal infinity is conformally flat. Interesting examples are discussed and a nonexistence theorem is proved using Killing spinors. In the second part we define mass for a manifold which is asymptotic to the hyperbolic space in a certain sense and prove the corresponding positive mass theorem using Killing spinors assuming the positive energy condition. At the end a Penrose-type conjecture is discussed.
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