Anisotropic curvature flow of immersed curves

On Anisotropic Curvature Flow Equations

We study the anisotropic flow V = bk where b > 0. We prove that if 13 < σ ≤ 1, only type I blow up occurs and if 0 < σ < 13 Type II blow up occurs. We also establish a prior estimates and existence of stationary solutions of self-similar curves and the existence of “ Abresch-Langer” type curves.

Discrete anisotropic curvature flow of graphs

© SMAI, EDP Sciences, 1999, tous droits réservés. L’accès aux archives de la revue « ESAIM: Modélisation mathématique et analyse numérique » (http://www.esaim-m2an.org/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce...

Solution and Application of Anisotropic Curvature Driven Evolution of Curves

Anisotropic and Crystalline Mean Curvature Flow

Cohomology and Immersed Curves

We introduce a new cohomology-theoretic method for classifying generic immersed curves in closed compact surfaces by using Gauss codes. This subsumes a result of J.S. Carter on classifying immersed curves in oriented compact surfaces, and provides a criterion for when an immersion is two-colorable. We note an application to twisted virtual link theory.