Gursky, Matthew J. (1991) Compactness of conformal metrics with integral bounds on curvature. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-06192007-145905
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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 [...] norm of the curvature tensor for fixed p > n/2 has a subsequence which converges in [...]. If n = 3, we have the same result if we assume, in addition, that the scalar curvature has an [...] 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.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Restricted to Caltech community only|
|Defense Date:||23 May 1991|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||12 Jul 2007|
|Last Modified:||26 Dec 2012 02:53|
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