Symmetric mean curvature flow on the n-sphere

2023/04/24 by Jingwen Chen, Chen, Jingwen · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2304.12282

openalex publication_date 2023/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we generalize our previous results joint with Pedro Gaspar to higher dimensions, prove the existence of (infinitely many) eternal weak mean curvature flows in Sⁿ⁺¹ (for all n ≥ 2) connecting a Clifford hypersurface S¹(√((1)/(n))) × S^n-1 (√((n-1)/(n))) to the equatorial spheres Sⁿ.

Cited by

• When can minimal hypersurfaces be connected by mean curvature flow?

Related

• Existence of Mean Curvature Flow Singularities with Bounded Mean Curvature
• Blow Up of Compact Mean Curvature Flow Solutions with Bounded Mean Curvature
• On the inverse mean curvature flow by parallel hypersurfaces in space forms
• Ancient solutions to mean curvature flow for isoparametric submanifolds
• Convex solutions to the mean curvature flow