Preserving curvature lower bounds when Ricci flowing non-smooth initial data
Abstract
In this paper we survey some results on Ricci flowing non-smooth initial data. Among other things, we give a non-exhaustive list of various weak initial data which can be evolved with the Ricci flow. We also survey results which show that various curvature lower bounds will, possibly up to a constant, be preserved, if we start with such possibly non-smooth initial data. Some proofs/proof sketches are given in certain cases. A list of some open problems related to these areas is given in the last section of the paper.
Cite
@article{arxiv.2411.13204,
title = {Preserving curvature lower bounds when Ricci flowing non-smooth initial data},
author = {Miles Simon},
journal= {arXiv preprint arXiv:2411.13204},
year = {2024}
}
Comments
This survey paper appeared in "Surveys in Differential Geometry, Vol. 27, No. 1 (2022), pp. 147-187". Although the reference is 2022, the paper was first submitted/published in 2024. In this version, Version 2: Fixed up a formatting error. Otherwise no changes to Version 1