Smoothing Riemannian Metrics with Bounded Ricci Curvatures in Dimension Four, II

Details Smoothing Riemannian Metrics with Bounded Ricci Curvatures in Dimension Four, II Smoothing Riemannian Metrics with Bounded Ricci Curvatures in Dimension Four, II

2009-11-16

arxiv.org/abs/0911.3104v1

Mathematics

Differential Geometry

17 pages

Scientific paper

This note is a continuation of the author's paper \cite{Li}. We prove that if the metric $g$ of a 4-manifold has bounded Ricci curvature and the curvature has no local concentration everywhere, then it can be smoothed to a metric with bounded sectional curvature. Here we don't assume the bound for local Sobolev constant of $g$ and hence this smoothing result can be applied to the collapsing case.

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