JournalsifbVol. 3 , No. 4DOI 10.4171/ifb/47

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

  • Giovanni Bellettini

    Università di Roma 'Tor Vergata', Italy
  • Matteo Novaga

    Università di Pisa, Italy
  • Maurizio Paolini

    Università Cattolica del Sacro Cuore, Brescia, Italy
Characterization of facet breaking for nonsmooth mean curvature flow in the convex case cover

Abstract

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.