Geodesic
Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature
Kybernetika, Tome 43 (2007) no. 6, pp. 903-912 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex: a solution polygon converges to the boundary of the Wulff shape without vanishing edges as time tends to infinity.
Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex: a solution polygon converges to the boundary of the Wulff shape without vanishing edges as time tends to infinity.
Classification : 34A26, 34A34, 34K25, 39A12, 53A04, 74N05, 82D25
Keywords: essentially admissible polygon; crystalline curvature; the Wulff shape; isoperimetric inequality 
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Yazaki, Shigetoshi. Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature. Kybernetika, Tome 43 (2007) no. 6, pp. 903-912. http://geodesic.mathdoc.fr/item/KYB_2007_43_6_a13/

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