English

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 κ\kappa-solution. We prove that the every noncompact ancient κ\kappa-solution in dimension 33 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