On the distance control problem in Ricci flows
Differential Geometry
2017-09-05 v3 Analysis of PDEs
Abstract
We show that the distance function under the Ricci flow is uniformly continuous in the time direction, assuming only the scalar curvature is bounded.
Keywords
Cite
@article{arxiv.1303.1895,
title = {On the distance control problem in Ricci flows},
author = {Gang Tian and Qi S. Zhang},
journal= {arXiv preprint arXiv:1303.1895},
year = {2017}
}
Comments
The paper is withdrawn due to a gap in the proof of Lemma 2.1 Note 2017/09/02. The gap is fixed and result extended in "Heat kernel and curvature bounds in Ricci flows with bounded scalar curvature", by R. Bamler and Q. S. Zhang, Adv. Math. (319) 2017, p396-450. We wish to thank R. Bamler for the help and G. Tian for the generosity for not being an author of the new paper