# Anisotropic curvature flow of immersed networks

created by novaga on 04 Dec 2020
modified on 02 Mar 2021

[BibTeX]

Accepted Paper

Inserted: 4 dec 2020
Last Updated: 2 mar 2021

Journal: Milan J. Math.
Year: 2020

ArXiv: 2012.02490 PDF

Abstract:

We consider motion by anisotropic curvature of a network of three curves immersed in the plane, meeting at a triple junction and with the other ends fixed. We show existence, uniqueness and regularity of a maximal geometric solution and we prove that, if the maximal time is finite, then either the length of one of the curves goes to zero or the $L^2$ norm of the anisotropic curvature blows up.