Facet-breaking for three dimensional crystals evolving by mean curvature

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

doi:10.4171/IFB/3

Facet-breaking for three dimensional crystals evolving by mean curvature

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

University of Rome Tor Vergata
University of Pisa

Research output: Contribution to journal › Article › peer-review

39 Citations (Scopus)

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.

Original language	English
Pages (from-to)	39-55
Number of pages	17
Journal	Interfaces and Free Boundaries
Volume	1
DOIs	https://doi.org/10.4171/IFB/3
Publication status	Published - 1999

Keywords

crystalline curvature

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10.4171/IFB/3

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title = "Facet-breaking for three dimensional crystals evolving by mean curvature",

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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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

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 -

Facet-breaking for three dimensional crystals evolving by mean curvature

Abstract

Keywords

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