Time zero regularity of Ricci flow
Differential Geometry
2022-10-27 v2 Analysis of PDEs
Abstract
We consider the problem of when a smooth Ricci flow, for positive time, that attains smooth initial data in a weak sense must be smooth down to the initial time. We obtain curvature estimates for an example where this fails. We prove a positive result in the case that the flow satisfies a lower IC1 curvature bound, equivalent to a lower Ricci bound in three dimensions. As an application, we prove that Gromov-Hausdorff limits of WPIC1 manifolds are WPIC1.
Cite
@article{arxiv.2202.12564,
title = {Time zero regularity of Ricci flow},
author = {Man-Chun Lee and Peter M. Topping},
journal= {arXiv preprint arXiv:2202.12564},
year = {2022}
}
Comments
Accepted to IMRN