Geodesic
Facet-breaking for three-dimensional crystals evolving by mean curvature
Giovanni Bellettini1 ; Matteo Novaga2 orcid ; Maurizio Paolini3
1Università di Roma 'Tor Vergata', Italy
2Università di Pisa, Italy
3Università Cattolica del Sacro Cuore, Brescia, Italy
Interfaces and free boundaries, Tome 1 (1999) no. 1, pp. 39-55

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DOI

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.
DOI : 10.4171/ifb/3
Classification : 46-XX, 60-XX
Mots-clés : Facet-breaking, three-dimensional crystals, mean curvature

Giovanni Bellettini  1   ; Matteo Novaga  2   ; Maurizio Paolini  3

1 Università di Roma 'Tor Vergata', Italy
2 Università di Pisa, Italy
3 Università Cattolica del Sacro Cuore, Brescia, Italy 
Giovanni Bellettini; Matteo Novaga; Maurizio Paolini. Facet-breaking for three-dimensional crystals evolving by mean curvature. Interfaces and free boundaries, Tome 1 (1999) no. 1, pp. 39-55. doi: 10.4171/ifb/3
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