Mean curvature flow solitons from symmetry group viewpoint

2022/11/12 by Xu Han, Han, Xu, Zhonghua Hou +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #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.2211.06577

openalex publication_date 2022/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The symmetry group of the mean curvature flow in general ambient Riemannian manifolds is determined, based on which we define generalized solitons to the mean curvature flow. We also provide examples of homothetic solitons in non-Euclidean surfaces and prove that all the affine solutions to the mean curvature flow are self-similar solutions.

Related

• Mean curvature flow solitons in the presence of conformal vector fields
• Translating solitons of the mean curvature flow in the space ℍ²×ℝ
• SO(2) symmetry of the translating solitons of the mean curvature flow in ℝ⁴
• On the topology of translating solitons of the mean curvature flow
• Some examples of self-similar solutions and translating solitons for mean curvature flow