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 (M,g) be a closed Riemannian manifold with dimension n > 2, and

{gk = uk 4 (n2) g}

be a noncollapsing conformal metric sequence with fixed volume. We prove that {log uk} is compact in C0,α(M) if Ric (gk)Lp(M,gk) is bounded, where p > n 2 .

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