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We study the evolution under the Ricci flow of surfaces with singularities of cone type. Firstly we provide a complete classification of gradient Ricci solitons on surfaces, which is of independent interest. Secondly, we prove that closed cone surfaces with cone angles less or equal to p converge, up to rescaling, to closed soliton metrics under the Ricci flow.
Cite this article
Daniel Ramos, Ricci flow on cone surfaces. Port. Math. 75 (2018), no. 1, pp. 11–65DOI 10.4171/PM/2010