# Analytic and geometric properties of generic Ricci solitons

created by catino on 25 Mar 2014
modified on 16 Sep 2016

[BibTeX]

Published Paper

Inserted: 25 mar 2014
Last Updated: 16 sep 2016

Journal: Trans. Amer. Math. Soc.
Volume: 368
Pages: 7533-7549
Year: 2016

Abstract:

The aim of this paper is to prove some classification results for generic shrinking Ricci solitons. In particular, we show that every three dimensional generic shrinking Ricci soliton is given by quotients of either $\mathbb{S}^3$, $\mathbb{R}\times\mathbb{S}^2$ or $\mathbb{R}^3$, under some very weak conditions on the vector field $X$ generating the soliton structure. In doing so we introduce analytical tools that could be useful in other settings; for instance we prove that the Omori-Yau maximum principle holds for the $X$-Laplacian on every generic Ricci soliton, without any assumption on $X$.