A uniform Sobolev inequality for Ricci flow with surgeries and applications

We prove a uniform Sobolev inequality for Ricci flow, which is independent of the number of surgeries. As an application, under less assumptions, a noncollapsing result stronger than Perelman's κ noncollapsing with surgery is derived. The proof is much shorter and seems more accessible. The result also improves some earlier ones where the Sobolev inequality depended on the number of surgeries. To cite this article: Q.S. Zhang, C. R. Acad. Sci. Paris, Ser. I 346 (2008).