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On a conformal Gauss-Bonnet-Chern in...

Fang, Hao.

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On a conformal Gauss-Bonnet-Chern inequality and analytic torsion for manifolds with boundary.

Record Type:	Electronic resources : Monograph/item
Title/Author:	On a conformal Gauss-Bonnet-Chern inequality and analytic torsion for manifolds with boundary./
Author:	Fang, Hao.
Description:	87 p.
Notes:	Source: Dissertation Abstracts International, Volume: 62-01, Section: B, page: 0278.
Contained By:	Dissertation Abstracts International62-01B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3001200
ISBN:	049309864X

On a conformal Gauss-Bonnet-Chern inequality and analytic torsion for manifolds with boundary.
Fang, Hao.

On a conformal Gauss-Bonnet-Chern inequality and analytic torsion for manifolds with boundary. - 87 p.

Source: Dissertation Abstracts International, Volume: 62-01, Section: B, page: 0278.

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

This dissertation contains two parts.

ISBN: 049309864XSubjects--Topical Terms:

515831
Mathematics.

On a conformal Gauss-Bonnet-Chern inequality and analytic torsion for manifolds with boundary.
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100 1 $a Fang, Hao. $3 1928540
245 1 0 $a On a conformal Gauss-Bonnet-Chern inequality and analytic torsion for manifolds with boundary.
300 $a 87 p.
500 $a Source: Dissertation Abstracts International, Volume: 62-01, Section: B, page: 0278.
500 $a Adviser: S.-Y. Chang.
502 $a Thesis (Ph.D.)--Princeton University, 2001.
520 $a This dissertation contains two parts.
520 $a In the first part, we study a class of conformally invariant operators P and their related conformally invariant curvatures Q on even-dimensional Riemannian manifolds. When the manifold is locally conformally flat (LCF) and compact without boundary, Q-curvature is naturally related to the integrand in the classical Gauss-Bonnet-Chern formula, i.e., the Pfaffian curvature (CF. [Br2, BrGP]). For a class of even-dimensional complete LCF manifolds with integrable Q-curvature, we establish a Gauss-Bonnet-Chern inequality. As applications, finiteness theorems for certain classes of complete LCF manifolds are also proven. These are extensions of the classical results of Cohn-Vossen [CV] and Huber [H] in dimension two and those of Chang-Qing-Yang [CQY1, CQY2] in dimension four.
520 $a In the second part, we study the analytic torsion of manifolds. On a closed Riemannian manifold, the analytic torsion of the metric is equal to a topological invariant, the Reidemeister torsion, by the celebrated Cheeger-Muller theorem (Cf. [C, Mu1]. For a manifold with boundary, the difference between these two torsions is discussed in [LR], [L] and [V], when the metric near the boundary has a product structure. We prove a general formula for the difference between analytic torsion and Reidemeister torsion on a manifold with boundary. We find that an extra term appears in the non-product case. Interestingly, this term is precisely the transgression of the Pfaffian in the even dimensional case; while in the odd dimensional case, it is a term involving the second fundamental form of the boundary and the curvature tensor of the manifold. This part of the dissertation has appeared in a joint work with X. Dai [DF].
590 $a School code: 0181.
650 4 $a Mathematics. $3 515831
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710 2 0 $a Princeton University. $3 645579
773 0 $t Dissertation Abstracts International $g 62-01B.
790 1 0 $a Chang, S.-Y., $e advisor
790 $a 0181
791 $a Ph.D.
792 $a 2001
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3001200