Curvature bounds for regularized riemannian metrics

2020/01/14 by Luckhardt, Daniel, Kordaß, Jan-Bernhard
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.05073

Abstract

We investigate regularization of riemannian metrics by mollification. Assuming both-sided bounds on the Ricci tensor and a lower injectivity radius bound we obtain a uniform estimate on the change of the sectional curvature. Actually, our result holds for any metric with a uniform bound on the W^2,p-harmonic radius.

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