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It is shown that a shrinking gradient Ricci soliton must be smoothly asymptotic to a cone if its Ricci curvature goes to zero at infinity.
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Ovidiu Munteanu, Jiaping Wang, Conical structure for shrinking Ricci solitons. J. Eur. Math. Soc. 19 (2017), no. 11, pp. 3377–3390DOI 10.4171/JEMS/741