Calculus of Variations and Geometric Measure Theory
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G. Catino - P. Mastrolia - D. D. Monticelli

Classification of expanding and steady Ricci solitons with integral curvature decay

created by catino on 07 Jan 2015
modified on 28 Jan 2017


Published Paper

Inserted: 7 jan 2015
Last Updated: 28 jan 2017

Journal: Geom. Topol.
Volume: 20
Number: 5
Pages: 2665-2685
Year: 2016


In this paper we prove new classification results for nonnegatively curved gradient expanding and steady Ricci solitons in dimension three and above, under suitable integral assumptions on the scalar curvature of the underlying Riemannian manifold. In particular we show that the only complete expanding solitons with nonnegative sectional curvature and integrable scalar curvature are quotients of the Gaussian soliton, while in the steady case we prove rigidity results under sharp integral scalar curvature decay. As a corollary, we obtain that the only three dimensional steady solitons with less than quadratic volume growth are quotients of $\erre^{3}$ or of $\erre\times\Sigma^{2}$, where $\Sigma^{2}$ is Hamilton's cigar.


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