Calculus of Variations and Geometric Measure Theory

J. Fischer - S. Hensel - A. Marveggio - M. Moser

Stability of multiphase mean curvature flow beyond circular topology changes

created by marveggio on 04 Apr 2024
modified on 11 Apr 2024



Inserted: 4 apr 2024
Last Updated: 11 apr 2024

Year: 2024

ArXiv: 2404.02884 PDF


We prove a weak-strong uniqueness principle for varifold-BV solutions to planar multiphase mean curvature flow beyond a circular topology change: Assuming that there exists a classical solution with an interface that becomes increasingly circular and shrinks to a point, any varifold-BV solution with the same initial interface must coincide with it, and any varifold-BV solution with similar initial data must undergo the same type of topology change. Our result illustrates the robustness of the relative energy method for establishing weak-strong uniqueness principles for interface evolution equations, showing that it may also be applied beyond certain topological changes.