Vol. 239, No. 1, 2009

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Strong noncollapsing and uniform Sobolev inequalities for Ricci flow with surgeries

Qi S. Zhang

Vol. 239 (2009), No. 1, 179–200
Abstract

We prove a uniform Sobolev inequality for Ricci flow that is independent of the number of surgeries. As an application, under fewer assumptions, we derive a noncollapsing result stronger than Perelman’s κ-noncollapsing result with surgery. 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.

Keywords
strong noncollapsing, Sobolev imbedding, Ricci flow, surgery
Mathematical Subject Classification 2000
Primary: 53C44
Milestones
Received: 29 July 2008
Revised: 15 September 2008
Accepted: 17 September 2008
Published: 1 January 2009
Authors
Qi S. Zhang
Department of Mathematics
University Of California
Riverside, CA 92521
United States