TY - JOUR
T1 - Facet-breaking for three dimensional crystals evolving by mean curvature
AU - Bellettini, G.
AU - Bellettini, Giovanni
AU - Novaga, M.
AU - Novaga, Matteo
AU - Paolini, Maurizio
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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.
KW - crystalline curvature
KW - crystalline curvature
UR - http://hdl.handle.net/10807/20938
U2 - 10.4171/IFB/3
DO - 10.4171/IFB/3
M3 - Article
SN - 1463-9963
VL - 1
SP - 39
EP - 55
JO - Interfaces and Free Boundaries
JF - Interfaces and Free Boundaries
ER -