SO(2) symmetry of the translating solitons of the mean curvature flow in ℝ⁴

2020/12/16 by Jingze Zhu, Zhu, Jingze · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Curvature #Differential Geometry (math.DG) #FOS: Mathematics #Flow (mathematics) #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Mean curvature #Mean curvature flow #Mean flow #Mechanics #Physics #Regular polygon #Symmetry (geometry) #math.DG

paper · pdf · doi:10.48550/arxiv.2012.09319

published in arXiv (Cornell University) (Cornell University) · Revised version, appeared in Annals of PDE

openalex publication_date 2020/12/16 · arxiv created 2023/01/02 · arxiv updated 2023/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we prove that the translating solitons of the mean curvature flow in ℝ⁴ which arise as blow up limit of embedded, mean convex mean curvature flow must have SO(2) symmetry.

Cited by

• Mean curvature flow through singularities
• Rotational symmetry of uniformly 3-convex translating solitons of mean curvature flow in higher dimensions
• Planarity and convexity for pinched ancient solutions of mean curvature flow

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