Integral estimates of conformal metrics

Xu, Xingwang

doi:10.1090/S0002-9939-96-03112-7

Integral estimates of conformal metrics
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Proc. Amer. Math. Soc. 124 (1996), 315-324 Request permission

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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