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We prove that in the absence of topological changes, the notion of BVsolutions to planar multiphase mean curvature flow does not allow for amechanism for (unphysical) non-uniqueness. Our approach is based on the localstructure of the energy landscape near a classical evolution by mean curvature.Mean curvature flow being the gradient flow of the surface energy functional,we develop a gradient-flow analogue of the notion of calibrations. Just likethe existence of a calibration guarantees that one has reached a global minimumin the energy landscape, the existence of a "gradient flow calibration" ensuresthat the route of steepest descent in the energy landscape is unique andstable.

The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions