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

Ye Li

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arXiv · 0911.3104

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

Ye Li

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Abstract

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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BibTeX RIS

Ye Li. 2009-11-16. Smoothing Riemannian Metrics with Bounded Ricci Curvatures in Dimension Four, II. https://arxiv.org/abs/0911.3104

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