Rotational symmetry of self-similar solutions to the Ricci flow
  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. 
S. Brendle
math.DG math.AP