Selfsimilar shrinking curves for anisotropic curvature flow equations

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.

Multifractal Formalism and Anisotropic Selfsimilar Functions

In this paper we prove that the conjectures of Frisch and Parisi in 9] and Arneodo et al in 1] (called the multifractal formalism for functions) may fail for some non homogenous selfsimilar functions in m dimension, m 2. In these cases, we compute the correct spectrum of singularities and we show how the multifractal formalism must be modiied.

Discrete anisotropic curvature flow of graphs

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Anisotropic and Crystalline Mean Curvature Flow

Solution and Application of Anisotropic Curvature Driven Evolution of Curves