CaltechTHESIS
  A Caltech Library Service

Compactness of Conformal Metrics with Integral Bounds on Curvature

Citation

Gursky, Matthew J. (1991) Compactness of Conformal Metrics with Integral Bounds on Curvature. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/00WZ-PH51. https://resolver.caltech.edu/CaltechETD:etd-06192007-145905

Abstract

In this thesis, we show that a sequence of conformal metrics on a compact n-dimensional Riemannian manifold (n ≥ 4) which has an upper bound on volume and an upper bound on the LP[...] norm of the curvature tensor for fixed p > n/2 has a subsequence which converges in Cα. If n = 3, we have the same result if we assume, in addition, that the scalar curvature has an L2 bound.

As corollaries, we have the compactness of a sequence of conformal metrics on a compact three-manifold which are isospectral with respect to either the standard or conformal Laplacian, and the result of Lelong-Ferrand that any compact manifold with non-compact conformal group is conformally equivalent to the standard sphere.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Chang, S. Y. A. (advisor)
  • Wolff, Thomas H. (co-advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:23 May 1991
Non-Caltech Author Email:mgursky (AT) nd.edu
Record Number:CaltechETD:etd-06192007-145905
Persistent URL:https://resolver.caltech.edu/CaltechETD:etd-06192007-145905
DOI:10.7907/00WZ-PH51
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2650
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:12 Jul 2007
Last Modified:21 Dec 2019 04:24

Thesis Files

[img]
Preview
PDF - Final Version
See Usage Policy.

1MB

Repository Staff Only: item control page