Facet-breaking for three-dimensional crystals evolving by mean curvature

  • Giovanni Bellettini

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

    Università di Pisa, Italy
  • Maurizio Paolini

    Università Cattolica del Sacro Cuore, Brescia, Italy


We show two examples of facet-breaking for three-dimensional polyhedral surfaces evolving by crystalline mean curvature. The analysis shows that creation of new facets during the evolution is a common phenomenon. The first example is completely rigorous, and the evolution after the subdivision of one facet is explicitly computed for short times. Moreover, the constructed evolution is unique among the crystalline flows with the given initial datum. The second example suggests that curved portions of the boundary may appear even starting from a polyhedral set close to the Wulff shape.

Cite this article

Giovanni Bellettini, Matteo Novaga, Maurizio Paolini, Facet-breaking for three-dimensional crystals evolving by mean curvature. Interfaces Free Bound. 1 (1999), no. 1, pp. 39–55

DOI 10.4171/IFB/3