Compactness of conformal metrics with integral bounds on Ricci curvature

be a noncollapsing conformal metric sequence with fixed volume. We prove that ${\log u_{k}}$ is compact in $C^{0, α} (M)$ if $∥ Ric (g_{k}) ∥_{L^{p} (M, g_{k})}$ is bounded, where $p > \frac{n}{2}$ .

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Keywords

conformal metric, integral Ricci curvature, blow-up

Mathematical Subject Classification

Primary: 53C21, 58J05

Milestones

Received: 2 April 2020

Revised: 12 November 2021

Accepted: 20 November 2021

Published: 26 February 2022

Authors

Conghan Dong
Mathematics Department Stony Brook University Stony Brook, NY United States

Yuxiang Li
Department of Mathematical Sciences Tsinghua University Beijing China

Vol. 316, No. 1, 2022

Conghan Dong and Yuxiang Li

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors