Preserving curvature lower bounds when Ricci flowing non-smooth initial data

Miles Simon

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arXiv · 2411.13204

Preserving curvature lower bounds when Ricci flowing non-smooth initial data

Miles Simon

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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.

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Miles Simon. 2024-11-20. Preserving curvature lower bounds when Ricci flowing non-smooth initial data. https://arxiv.org/abs/2411.13204

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