Geodesic
Characterization of facet breaking for nonsmooth mean curvature flow in the convex case
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 3 (2001) no. 4, pp. 415-446

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DOI

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.
DOI : 10.4171/ifb/47
Classification : 46-XX, 60-XX
Mots-clés : Crystalline mean curvature, anisotropic evolutions, calibrable facet

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. Characterization of facet breaking for nonsmooth mean curvature flow in the convex case. Interfaces and free boundaries, Tome 3 (2001) no. 4, pp. 415-446. doi: 10.4171/ifb/47
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     title = {Characterization of facet breaking for nonsmooth mean curvature flow in the convex case},
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     pages = {415--446},
     year = {2001},
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     doi = {10.4171/ifb/47},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/47/}
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