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.

arXiv commentThis 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

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