Minimally invasive surgery for Ricci flow singularities
Differential Geometry
2009-07-03 v1 Analysis of PDEs
Abstract
In this paper, we construct smooth forward Ricci flow evolutions of singular initial metrics resulting from rotationally symmetric neckpinches on S^(n+1), without performing an intervening surgery. In the restrictive context of rotational symmetry, this construction gives evidence in favor of Perelman's hope for a "canonically defined Ricci flow through singularities".
Keywords
Cite
@article{arxiv.0907.0232,
title = {Minimally invasive surgery for Ricci flow singularities},
author = {Sigurd B. Angenent and M. Cristina Caputo and Dan Knopf},
journal= {arXiv preprint arXiv:0907.0232},
year = {2009}
}