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Ricci Yang-Mills flow.

Streets, Jeffrey D.

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Ricci Yang-Mills flow.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Ricci Yang-Mills flow./
Author:	Streets, Jeffrey D.
Description:	142 p.
Notes:	Adviser: Mark A. Stern.
Contained By:	Dissertation Abstracts International68-02B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3254891

Ricci Yang-Mills flow.
Streets, Jeffrey D.

Ricci Yang-Mills flow. - 142 p.

Adviser: Mark A. Stern.

Thesis (Ph.D.)--Duke University, 2007.

Let (Mn, g) be a Riemannian manifold. Say K → E → M is a principal K -bundle with connection A. We define a natural evolution equation for the pair (g, A) combining the Ricci flow for g and the Yang-Mills flow for A which we dub Ricci Yang-Mills flow. We show that these equations are, up to diffeomorphism equivalence, the gradient flow equations for a Riemannian functional on M. Associated to this energy functional is an entropy functional which is monotonically increasing in areas close to a developing singularity. This entropy functional is used to prove a non-collapsing theorem for certain solutions to Ricci Yang-Mills flow.Subjects--Topical Terms:

515831
Mathematics.

Ricci Yang-Mills flow.
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005 20110624
008 110624s2007 ||||||||||||||||| ||eng d
035 $a (UMI)AAI3254891
035 $a AAI3254891
040 $a UMI $c UMI
100 1 $a Streets, Jeffrey D. $3 1279905
245 1 0 $a Ricci Yang-Mills flow.
300 $a 142 p.
500 $a Adviser: Mark A. Stern.
500 $a Source: Dissertation Abstracts International, Volume: 68-02, Section: B, page: 1015.
502 $a Thesis (Ph.D.)--Duke University, 2007.
520 $a Let (Mn, g) be a Riemannian manifold. Say K → E → M is a principal K -bundle with connection A. We define a natural evolution equation for the pair (g, A) combining the Ricci flow for g and the Yang-Mills flow for A which we dub Ricci Yang-Mills flow. We show that these equations are, up to diffeomorphism equivalence, the gradient flow equations for a Riemannian functional on M. Associated to this energy functional is an entropy functional which is monotonically increasing in areas close to a developing singularity. This entropy functional is used to prove a non-collapsing theorem for certain solutions to Ricci Yang-Mills flow.
520 $a We show that these equations, after an appropriate change of gauge, are equivalent to a strictly parabolic system, and hence prove general unique short-time existence of solutions. Furthermore we prove derivative estimates of Bernstein-Shi type. These can be used to find a complete obstruction to long-time existence, as well as to prove a compactness theorem for Ricci Yang Mills flow solutions.
520 $a Our main result is a fairly general long-time existence and convergence theorem for volume-normalized solutions to Ricci Yang-Mills flow. The limiting pair (g, A) satisfies equations coupling the Einstein and Yang-Mills conditions on g and A respectively. Roughly these conditions are that the associated curvature F A must be large, and satisfy a certain "stability" condition determined by a quadratic action of FA on symmetric two-tensors.
590 $a School code: 0066.
650 4 $a Mathematics. $3 515831
650 4 $a Physics, Theory. $3 1019422
690 $a 0405
690 $a 0753
710 2 $a Duke University. $3 569686
773 0 $t Dissertation Abstracts International $g 68-02B.
790 $a 0066
790 1 0 $a Stern, Mark A., $e advisor
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3254891