Facet-breaking for three-dimensional crystals evolving by mean curvature
type: Item
instance of: scholarly article
title: Facet-breaking for three-dimensional crystals evolving by mean curvature
zbMATH Open document ID: 0934.49023
DOI: 10.4171/IFB/3
published in: Interfaces and Free Boundaries
publication date: 2000-04-03T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 49Q10
zbMATH DE Number: 1334697
zbMATH Keywords: facet-breaking
zbMATH Keywords: polyhedral surfaces
zbMATH Keywords: crystalline mean curvature
zbMATH Keywords: crystalline flows
zbMATH Keywords: Wulff shape
author: Giovanni Bellettini
author: M. Novaga
author: Maurizio Paolini
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1334697