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On the geometry of conformally compa...

Wang, Xiaodong.

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On the geometry of conformally compact Einstein manifolds.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On the geometry of conformally compact Einstein manifolds./
Author:	Wang, Xiaodong.
Description:	81 p.
Notes:	Adviser: Richard Schoen.
Contained By:	Dissertation Abstracts International62-09B.
Subject:	Mathematics. -
Online resource:	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.
LDR:01923nam 2200265 a 45 001 973860
005 20110928
008 110928s2001 eng d
020 $a 9780493383675
035 $a (UnM)AAI3026929
035 $a AAI3026929
040 $a UnM $c UnM
100 1 $a Wang, Xiaodong. $3 1262922
245 1 0 $a On the geometry of conformally compact Einstein manifolds.
300 $a 81 p.
500 $a Adviser: Richard Schoen.
500 $a Source: Dissertation Abstracts International, Volume: 62-09, Section: B, page: 4046.
502 $a Thesis (Ph.D.)--Stanford University, 2001.
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.
590 $a School code: 0212.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a Stanford University. $3 754827
773 0 $t Dissertation Abstracts International $g 62-09B.
790 $a 0212
790 1 0 $a Schoen, Richard, $e advisor
791 $a Ph.D.
792 $a 2001
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3026929