Two-Dimensional Gradient Ricci Solitons Revisited

2013/03/28 by Jacob Bernstein, Thomas Mettler · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Curvature #Geometric Analysis and Curvature Flows #Negative curvature #Nonlinear Partial Differential Equations #Ricci curvature #Ricci flow #Soliton #math.DG #msc:53C44

paper · pdf · doi:10.1093/imrn/rnt177

published as Int. Math. Res. Not. 2015 (2015), no. 1, 78-98 · 15 pages, 3 figures. Corrected statement and proof of Theorem 2 and removed Corollary 1

arxiv created 2013/03/28 · openalex publication_date 2013/09/06 · arxiv updated 2015/03/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this note, we complete the classification of the geometry of non-compact two-dimensional gradient Ricci solitons. As a consequence, we obtain two corollaries: First, a complete two-dimensional gradient Ricci soliton has bounded curvature. Second, we give examples of complete two-dimensional expanding Ricci solitons with negative curvature that are topologically disks and are not hyperbolic space.

Citations

• The Ricci flow on the 2-sphere

Cited by

• Rotational symmetry of conical Kähler–Ricci solitons
• RICCI FLOWS ON SURFACES RELATED TO THE EINSTEIN WEYL AND ABELIAN VORTEX EQUATIONS
• Classification of expanding and steady Ricci solitons with integral curvature decay