Ancient solutions to the Ricci flow in dimension 3
Differential Geometry
2020-04-21 v3
Abstract
It is known from work of Perelman that any finite-time singularity of the Ricci flow on a compact three-manifold is modeled on an ancient -solution. We prove that the every noncompact ancient -solution in dimension is isometric to either the shrinking cylinders (or a quotient thereof), or the Bryant soliton.
Keywords
Cite
@article{arxiv.1811.02559,
title = {Ancient solutions to the Ricci flow in dimension 3},
author = {S. Brendle},
journal= {arXiv preprint arXiv:1811.02559},
year = {2020}
}
Comments
revised version, to appear in Acta Mathematica