Strong Non-collapsing and Uniform Sobolev Inequalities for Ricci Flow with Surgeries
نویسنده
چکیده
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 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.
منابع مشابه
Time-dependent Sobolev Inequality along the Ricci Flow
d dt g = −2Rc g(0) = g0 on a closed manifold M. An important ingredient of Perelman’s proof of geometrization conjecture is the non-collapsing theorem of Ricci flow which makes sure that we can get a singularity model of the flow when a singularity exists. In [7], Zhang gave an easier way to prove the noncollapsing theorem of Ricci flow via a uniform Sobolev inequality along the flow. Unfortuna...
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