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arXiv · 2404.02884

Stability of multiphase mean curvature flow beyond circular topology changes

Julian Fischer·Sebastian Hensel·Alice Marveggio·Maximilian Moser
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Abstract

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.

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Julian Fischer, Sebastian Hensel, Alice Marveggio, Maximilian Moser. 2024-04-03. Stability of multiphase mean curvature flow beyond circular topology changes. https://arxiv.org/abs/2404.02884

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