# Integral pinched shrinking Ricci solitons

created by catino on 24 Sep 2015
modified on 25 Aug 2016

[BibTeX]

Published Paper

Inserted: 24 sep 2015
Last Updated: 25 aug 2016

We prove that a $n$-dimensional, $4 \leq n \leq 6$, compact gradient shrinking Ricci soliton satisfying a $L^{n/2}$-pinching condition is isometric to a quotient of the round $\mathbb{S}^{n}$. The proof relies mainly on sharp algebraic curvature estimates, the Yamabe-Sobolev inequality and an improved rigidity result for integral pinched Einstein metrics.