Facet-breaking for three dimensional crystals evolving by mean curvature

Maurizio Paolini; Giovanni Bellettini; Matteo Novaga; G. Bellettini; M. Novaga

Facet-breaking for three dimensional crystals evolving by mean curvature

Maurizio Paolini, Giovanni Bellettini, Matteo Novaga, G. Bellettini, M. Novaga

Risultato della ricerca: Contributo in rivista › Articolo in rivista › peer review

Abstract

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.

Lingua originale	English
pagine (da-a)	39-55
Numero di pagine	17
Rivista	Interfaces and Free Boundaries
Stato di pubblicazione	Pubblicato - 1999

Keywords

crystalline curvature

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abstract = "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.",

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author = "Maurizio Paolini and Giovanni Bellettini and Matteo Novaga and G. Bellettini and M. Novaga",

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T1 - Facet-breaking for three dimensional crystals evolving by mean curvature

AU - Paolini, Maurizio

AU - Bellettini, Giovanni

AU - Novaga, Matteo

AU - Bellettini, G.

AU - Novaga, M.

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

UR - http://hdl.handle.net/10807/20938

M3 - Article

SP - 39

EP - 55

JO - Interfaces and Free Boundaries

JF - Interfaces and Free Boundaries

SN - 1463-9963

ER -