Perelman's reduced volume and a gap theorem for the Ricci flow
Differential Geometry
2009-09-01 v3
Abstract
In this paper, we show that any ancient solution to the Ricci flow with the reduced volume whose asymptotic limit is sufficiently close to that of the Gaussian soliton is isometric to the Euclidean space for all time. This is a generalization of Anderson's result for Ricci-flat manifolds. As a corollary, a gap theorem for gradient shrinking Ricci solitons is also obtained.
Keywords
Cite
@article{arxiv.0808.0303,
title = {Perelman's reduced volume and a gap theorem for the Ricci flow},
author = {Takumi Yokota},
journal= {arXiv preprint arXiv:0808.0303},
year = {2009}
}
Comments
final version