Strong non-collapsing and uniform Sobolev inequalities for Ricci flow with surgeries

Details Strong non-collapsing and uniform Sobolev inequalities for Ricci flow with surgeries Strong non-collapsing and uniform Sobolev inequalities for Ricci flow with surgeries

2007-12-09

arxiv.org/abs/0712.1329v1

Mathematics

Differential Geometry

Scientific paper

We prove a uniform Sobolev inequality for Ricci flow, which is independent of the number of surgeries. As an application, under less assumptions, a non-collapsing result stronger than Perelman's $\kappa$ non-collapsing with surgery is derived. The proof is shorter and seems more accessible. The result also improves some earlier ones where the Sobolev inequality depended on the number of surgeries.

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