Characterization of facet-breaking for nonsmooth mean curvature flow in the convex case

We investigate the breaking and bending phenomena of a facet of a three-dimensional crystal which evolves under crystalline mean curvature flow. We give necessary and sufficient conditions for a facet to be calibrable, i.e. not to break or bend under the evolution process. We also give a criterion which allows us to predict exactly where a subdivision of a non-calibrable facet takes place in the evolution process.

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