Smoothing metrics on closed Riemannian manifolds through the Ricci flow

Yunyan Yang

Smoothing metrics on closed Riemannian manifolds through the Ricci flow

Differential Geometry 2011-04-12 v1

Authors: Yunyan Yang

Abstract

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).

Keywords

Ricci flow Riemannian metric smoothing sectional curvature bound Sobolev inequality Ricci curvature a priori estimates

Cite

@article{arxiv.1104.1702,
  title  = {Smoothing metrics on closed Riemannian manifolds through the Ricci flow},
  author = {Yunyan Yang},
  journal= {arXiv preprint arXiv:1104.1702},
  year   = {2011}
}

Comments

14 pages

Related papers

View all related →