Motion of non-convex polygons by crystalline curvature and almost convexity phenomena

The behavior of solution polygons to generalized crystalline curvature flow is discussed. The conditions to guarantee that the solution polygon keeps its admissibility as long as enclosed area of solution polygon is positive are clarified. We also show that the solution polygon becomes “almost conve...

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Bibliographic Details
Published in:	Japan journal of industrial and applied mathematics Vol. 25; no. 2; pp. 233 - 253
Main Author:	Ishiwata, Tetsuya
Format:	Journal Article
Language:	English
Published:	Tokyo Springer-Verlag 01-06-2008 Springer Nature B.V Japan Society for Industrial and Applied Mathematics
Subjects:	Applications of Mathematics Computational Mathematics and Numerical Analysis convexity phenomena edge-disappearing Mathematics Mathematics and Statistics motion by crystalline curvature non-convex polygon motion by crystalline curvature non-convex polygon convexity phenomena edge-disappearing
Online Access:	Get full text
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Summary:	The behavior of solution polygons to generalized crystalline curvature flow is discussed. The conditions to guarantee that the solution polygon keeps its admissibility as long as enclosed area of solution polygon is positive are clarified. We also show that the solution polygon becomes “almost convex” before the extinction time.
ISSN:	0916-7005 1868-937X
DOI:	10.1007/BF03167521