Motion by curvature of planar networks II

2013/01/15 by Annibale Magni, Magni, Annibale, Carlo Mantegazza +3
Mathematics · #Stochastic processes and statistical mechanics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1301.3352

Abstract

We prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists smooth until the lengths of the three curves stay far from zero. If this is the case for all times, then the evolution exists for all times and the network converges to the Steiner minimal connection between the three endpoints.

Related

• Lectures on curvature flow of networks
• Evolution of networks with multiple junctions
• Nonlinear stability of stationary solutions for curvature flow with triple junction
• Existence and Uniqueness of the Motion by Curvature of regular networks
• Anisotropic curvature flow of immersed networks