arXiv Analytics

Sign in

arXiv:1603.08726 [math.DG]AbstractReferencesReviewsResources

Short-time existence of the Ricci flow on complete, non-collapsed $3$-manifolds with Ricci curvature bounded from below

Raphael Hochard

Published 2016-03-29Version 1

We prove that for any complete three-manifold with a lower Ricci curvature bound and a lower bound on the volume of balls of radius one, a solution to the Ricci flow exists for short time. Actually our proof also yields a (non-canonical) way to flow and regularize some interior region of a non-complete initial data satisfying the aformentioned bounds.

Comments: 39 pages, 6 figures
Categories: math.DG
Subjects: 53C44
Related articles: Most relevant | Search more
arXiv:math/0211230 [math.DG] (Published 2002-11-14)
A lower bound for the diameter of solutions to the Ricci flow with nonzero $H^{1}(M^{n};R)$
arXiv:math/0609725 [math.DG] (Published 2006-09-26, updated 2008-01-19)
On the lower bound of the K energy and F functional
arXiv:1406.0317 [math.DG] (Published 2014-06-02)
A lower bound for the number of negative eigenvalues of Schrödinger operators

Links

Toolbox