English

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

Differential Geometry 2007-12-11 v1 Analysis of PDEs

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 κ\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.

Keywords

Cite

@article{arxiv.0712.1329,
  title  = {Strong non-collapsing and uniform Sobolev inequalities for Ricci flow with surgeries},
  author = {Qi S. Zhang},
  journal= {arXiv preprint arXiv:0712.1329},
  year   = {2007}
}