Published Paper
Inserted: 24 sep 2015
Last Updated: 25 aug 2016
Journal: Adv. Math.
Volume: 303
Pages: 279-294
Year: 2016
Abstract:
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.
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