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Rotational symmetry of self-similar solutions to the Ricci flow

Published 6 Feb 2012 in math.DG and math.AP | (1202.1264v3)

Abstract: Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and \kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.

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