Smoothing metrics on closed Riemannian manifolds through the Ricci flow

Details Smoothing metrics on closed Riemannian manifolds through the Ricci flow Smoothing metrics on closed Riemannian manifolds through the Ricci flow

2011-04-09

arxiv.org/abs/1104.1702v1

Mathematics

Differential Geometry

14 pages

Scientific paper

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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