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Compactness of Conformal Metrics with Integral Bounds on Curvature


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.


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)
Record Number:CaltechETD:etd-06192007-145905
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2650
Deposited By: Imported from ETD-db
Deposited On:12 Jul 2007
Last Modified:21 Dec 2019 04:24

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