Rotational symmetry of self-similar solutions to the Ricci flow

Abstract

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and κ-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.

Final version, to appear in Invent. Math