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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Integral estimates of conformal metrics


Author: Xingwang Xu
Journal: Proc. Amer. Math. Soc. 124 (1996), 315-324
MSC (1991): Primary 58G25, 53C21
MathSciNet review: 1301536
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Abstract: In this article we show that there exists a rational number $\mu $, depending only on the dimension $n\ (\ge 5)$ of the manifold such that the $\mu $th-power of the conformal factor is bounded in $H^2_2$ norm in terms of volume bound and the square norm bound of the scalar curvature of the conformal metrics. Some applications are also given.


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Additional Information

Xingwang Xu
Affiliation: address Department of Mathematics, National University of Singapore, Singapore 0511
Email: matxuxw@leonis.nus.sg

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03112-7
PII: S 0002-9939(96)03112-7
Received by editor(s): June 22, 1994
Communicated by: \commby Peter Li
Article copyright: © Copyright 1996 American Mathematical Society