On the stability of m-fold circles and the dynamics of generalized curve shortening flows

2012/07/11 by Jean C. Cortissoz, Jean Cortissoz, Cortissoz, Jean +2
Mathematics · #35K55 #54C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.AP #math.DG #msc:35K55 #msc:54C44

paper · pdf · doi:10.48550/arxiv.1207.2698

13 pages; Comments, suggestions and criticisms more than welcome. some sections have been rewritten and another was added; some notational changes have been made; title has changed

openalex publication_date 2012/07/11 · arxiv created 2012/09/11 · arxiv updated 2012/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the (asymptotic and exponential) stability of the m-fold circle as a solution of the p-curve shortening flow (p≥ 1 an integer).

Related

• The blow up analysis of the general curve shortening flow
• Stabilization technique applied to curve shortening flow in the plane
• Stability of geometric flows on the circle
• On the rate of convergence of the p-curve shortening flow
• Stabilization technique applied to curve shortening flow in ℝ³