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