Weak-strong uniqueness for the mean curvature flow of double bubbles

Abstract

We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478v2] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions.

59 pages, corrected typos and some references, slightly revised regularity requirement in item i) of Definition 2 (gradient-flow calibration); results unchanged