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. (2020) for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions.
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Sebastian Hensel, Tim Laux, Weak-strong uniqueness for the mean curvature flow of double bubbles. Interfaces Free Bound. (2022),DOI 10.4171/IFB/484