Smoothing metrics on closed Riemannian manifolds through the Ricci flow

2011/04/09 by Yunyan Yang, Yang, Yunyan
Mathematics · #53C20 #53C21 #58J35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1104.1702

openalex publication_date 2011/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Under the assumption of the uniform local Sobolev inequality, it is proved that Riemannian metrics with an absolute Ricci curvature bound and a small Riemannian curvature integral bound can be smoothed to having a sectional curvature bound. This partly extends previous a priori estimates of Ye Li (J. Geom. Anal. 17 (2007) 495-511; Advances in Mathematics 223 (2010) 1924-1957).

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