Smoothing Riemannian metrics with bounded Ricci curvatures in dimension four, II

被引：2

作者：

Li, Ye ^{[1
]}

机构：

[1] Duke Univ, Dept Math, Durham, NC 27708 USA

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2012年 / 41卷 / 04期

关键词：

Ricci flow; Short-time existence; Smoothing Riemannian metrics in dimension four; UNIFORMLY ELLIPTIC-OPERATORS;

D O I：

10.1007/s10455-011-9290-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This note is a continuation of the author's paper (Li, Adv. Math. 223(6):1924-1957, 2010). We prove that if the metric g of a compact 4-manifold has bounded Ricci curvature and its 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.

引用

页码：407 / 421

页数：15

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