Ricci flow and PIC1

Peter M. Topping

Ricci flow and PIC1

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arxiv 2309.00596 v1 pith:YRHMHQSS submitted 2023-09-01 math.DG

Peter M. Topping This is my paper · ORCID

classification math.DG

keywords curvaturepositiveflownotionpic1problemsricciadapted

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We survey several problems concerning Riemannian manifolds with positive curvature of one form or another. We describe the PIC1 notion of positive curvature and argue that it is often the sharp notion of positive curvature to consider. Finally we explain how recent Ricci flow theory is particularly well adapted to solve these problems.

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Preserving curvature lower bounds when Ricci flowing non-smooth initial data
math.DG 2024-11 conditional novelty 1.0 of 10

A survey of results on Ricci flow from non-smooth initial data, focusing on preservation of lower curvature bounds and open problems.

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