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

TL;DR

This paper establishes a uniform Sobolev inequality for Ricci flow with surgeries, leading to a stronger non-collapsing result that improves upon previous bounds and is more accessible to proof techniques.

Contribution

It introduces a uniform Sobolev inequality for Ricci flow with surgeries that does not depend on the number of surgeries, enhancing non-collapsing results.

Findings

Proves a uniform Sobolev inequality independent of surgeries

Derives a stronger non-collapsing result than Perelman's

Provides a shorter, more accessible proof

Abstract

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.