Rotationally symmetric Ricci Flow on ℝⁿ⁺¹

2025/05/29 by M. Y. Hsiao, Hsiao, Ming
Mathematics · #53E20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2505.23157

openalex publication_date 2025/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a short-time existence theory for complete Ricci flows under scaling-invariant curvature bounds, starting from rotationally symmetric metrics on ℝⁿ⁺¹ that are noncollapsed at infinity, without assuming bounded curvature. As a consequence, we construct a complete Ricci flow solution coming out of a rotationally symmetric metric, which has a cone-like singularity at the origin and no minimal hypersphere centered at the origin, using an approximation method.

Citations

• Uniqueness of Ricci flow with scaling invariant estimates
• Three-manifolds with non-negatively pinched Ricci curvature
• Canonical surgeries in rotationally invariant Ricci flow
• Smoothing a measure on a Riemann surface using Ricci flow
• Some local Maximum principles along Ricci Flow
• On the regularity of Ricci flows coming out of metric spaces
• Ricci flow under local almost non-negative curvature conditions
• Local control on the geometry in 3D Ricci flow
• Uniqueness of the Ricci Flow on Complete Noncompact Manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci flow with surgery on three-manifolds

Related

• Some Type I solutions of Ricci flow with rotational symmetry
• On the Ricci flow on the rotationally symmetric two-ball
• Canonical surgeries in rotationally invariant Ricci flow
• Ricci flow neckpinches without rotational symmetry
• The Ricci flow on surfaces with boundary