Alexandria Digital Research Library

Poincare inequalities under gauge transformations

Author:
Wirts, Shawn Steven
Degree Grantor:
University of California, Santa Barbara. Mathematics
Degree Supervisor:
Denis Labutin
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2015
Issued Date:
2015
Topics:
Mathematics
Keywords:
Manifolds
Vector bundles
Partial differential equations
Gauge theory
Genres:
Dissertations, Academic and Online resources
Dissertation:
Ph.D.--University of California, Santa Barbara, 2015
Description:

For connections on trivial vector bundles compatible with compact gauge groups, we establish conditions on the vector bundle and gauge group under which translation of a connection by a constant connection matrix is achievable by a gauge transformation. These conditions may be roughly characterized as either restricting the base manifold to be one-dimensional or restricting the gauge group to take values in an abelian Lie group. These results are then used to prove Poincare inequalities on the gauge equivalent connection matrices, with some additional refinement of these results when the data considered is compactly supported and Coulomb.

Physical Description:
1 online resource (89 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3qz2858
ISBN:
9781339218083
Catalog System Number:
990045866240203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Shawn Wirts
File Description
Access: Public access
Wirts_ucsb_0035D_12654.pdf pdf (Portable Document Format)