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

References in corpus (1)

• On the uniqueness of smooth, stationary black holes in vacuum

Cited by in corpus (17)

• Geometry of shrinking Ricci solitons
• Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions
• Uniqueness of compact ancient solutions to three-dimensional Ricci flow
• Uniqueness of the bowl soliton
• Classification of expanding and steady Ricci solitons with integral curvature decay
• Rotational Symmetry of Conical Kähler-Ricci Solitons
• The Weyl Tensor of Gradient Ricci Solitons
• Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions
• Curvature growth of some 4-dimensional gradient Ricci soliton singularity models
• On a isoperimetric-isodiametric inequality
• On Complete Gradient Steady Ricci Solitons with Vanishing D-tensor
• Existence of singular rotationally symmetric gradient Ricci solitons in higher dimensions
• O(2)-symmetry of 3D steady gradient Ricci solitons
• Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature
• Cohomogeneity two Ricci solitons with sub-Euclidean volume
• On some locally symmetric embedded spaces with non-negative scalar curvature and their characterization
• Rigidity results on gradient Schouten solitons