Differential Geometry
A uniform Sobolev inequality for Ricci flow with surgeries and applications
Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 549-552.

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.

Nous prouvons une inégalité de Sobolev uniforme pour le flot de Ricci, indépendante du nombre de chirurgies. Comme application, nous établissons, avec moins d'hypothèses, un résultat de non-explosion plus fort que celui de Perelman sur la non-explosion de κ avec chirurgie. La preuve est plus courte et semble plus accessible. Le résultat améliore également des résultats antérieurs où l'inégalité de Sobolev dépendait du nombre de chirurgies.

Received:
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Published online:
DOI: 10.1016/j.crma.2008.03.016
Zhang, Qi S. 1

1 Department of Mathematics, University of California, Riverside, CA 92521, USA
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Zhang, Qi S. A uniform Sobolev inequality for Ricci flow with surgeries and applications. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 549-552. doi : 10.1016/j.crma.2008.03.016. http://www.numdam.org/articles/10.1016/j.crma.2008.03.016/

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