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

DOI10.1007/BF03167521zbMath1155.53033MaRDI QIDQ946859

Tetsuya Ishiwata

Publication date: 25 September 2008

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

non-convex polygonmotion by crystalline curvatureconvexity phenomenaedge-disappearing

Mathematics Subject Classification ID

Related Items (7)

Crystalline motion of spiral-shaped polygonal curves with a tip motion ⋮ A fast blow-up solution and degenerate pinching arising in an anisotropic crystalline motion ⋮ Motion by crystalline-like mean curvature: A survey ⋮ Periodic total variation flow of non-divergence type in \(\mathbb R^n\) ⋮ Very singular diffusion equations: second and fourth order problems ⋮ On spiral solutions to generalized crystalline motion with a rotating tip motion ⋮ Crystalline flow starting from a general polygon

Cites Work

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• Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface
• The heat equation shrinks embedded plane curves to round points
• Asymptotic behavior of solutions to a crystalline flow
• On the blow-up rate for fast blow-up solutions arising in an anisotropic crystalline motion.
• Two examples of nonconvex self-similar solution curves for a crystalline curvature flow
• Regularity and Convergence of Crystalline Motion
• A convexity theorem for a class of anisotropic flows of plane curves

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