#### Vol. 316, No. 1, 2022

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Compactness of conformal metrics with integral bounds on Ricci curvature

### Conghan Dong and Yuxiang Li

Vol. 316 (2022), No. 1, 65–79
##### Abstract

Let $\left(M,g\right)$ be a closed Riemannian manifold with dimension $n>2$, and

 $\left\{{g}_{k}={u}_{k}^{\frac{4}{\left(n-2\right)}}g\right\}$

be a noncollapsing conformal metric sequence with fixed volume. We prove that $\left\{\mathrm{log}{u}_{k}\right\}$ is compact in ${C}^{0,\alpha }\left(M\right)$ if $\parallel \mathrm{Ric}\left({g}_{k}\right){\parallel }_{{L}^{p}\left(M,{g}_{k}\right)}$ is bounded, where $p>\frac{n}{2}$.

##### Keywords
conformal metric, integral Ricci curvature, blow-up
##### Mathematical Subject Classification
Primary: 53C21, 58J05