Ricci Flow of regions with curvature bounded below in dimension three
Abstract
We consider smooth complete solutions to Ricci flow with bounded curvature on manifolds without boundary in dimension three. Assuming an open ball at time zero of radius one has curvature bounded from below by -1, then we prove estimates which show that compactly contained subregions of this ball will be smoothed out by the Ricci flow for a short but well defined time interval. The estimates we obtain depend only on the initial volume of the ball and the distance from the compact region to the boundary of the initial ball. Versions of these estimates for balls of radius r follow using scaling arguments.
Keywords
Cite
@article{arxiv.1407.1251,
title = {Ricci Flow of regions with curvature bounded below in dimension three},
author = {Miles Simon},
journal= {arXiv preprint arXiv:1407.1251},
year = {2017}
}
Comments
Journal version (2017, 'Journal of Geometric Analysis'). There are changes to notation. I included two new lemmata, Lemma 3.3 and 3.4, the content of which was previously in the proof of Theorem 1.6. New Remark, Remark 4.2, explains in more detail, how the constants appearing in the proof of Theorem 1.6 are chosen