A survey of results on Ricci flow from non-smooth initial data, focusing on preservation of lower curvature bounds and open problems.
Ricci-Deturck flow from rough metrics and applications
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abstract
Motivated by the recent work of Lamm and Simon, in this work we study the short-time existence theory of Ricci-Deturck flow starting from rough metrics which are bi-Lipschitz and have small local scaling invariant gradient concentration. As applications, we use it to study several stability problems related to the scalar curvature.
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math.DG 1years
2024 1verdicts
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Preserving curvature lower bounds when Ricci flowing non-smooth initial data
A survey of results on Ricci flow from non-smooth initial data, focusing on preservation of lower curvature bounds and open problems.