Ricci Yang-Mills Flow

dc.contributor.advisor

Stern, Mark A

dc.contributor.advisor

Bray, Hubert L

dc.contributor.advisor

Bryant, Robert L

dc.contributor.advisor

Saper, Leslie D

dc.contributor.author

Streets, Jeffrey D.

dc.date.accessioned

2007-05-04T17:37:34Z

dc.date.available

2007-05-04T17:37:34Z

dc.date.issued

2007-05-04T17:37:34Z

dc.department

Mathematics

dc.description.abstract

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 di eomorphism 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. 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. 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 FA must be large, and satisfy a certain “stability” condition determined by a quadratic action of FA on symmetric two-tensors.

dc.identifier.uri

https://hdl.handle.net/10161/192

dc.language.iso

en_US

dc.rights.uri

http://rightsstatements.org/vocab/InC/1.0/

dc.subject

riemannian manifold

dc.subject

Global differential geometry

dc.subject

Ricci flow

dc.subject

Yang-Mills theory

dc.title

Ricci Yang-Mills Flow

dc.type

Dissertation

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
D_Streets_Jeffrey_a_052007.pdf
Size:
499.88 KB
Format:
Adobe Portable Document Format

Collections