Calculus of Variations and Geometric Measure Theory

H. Kröner - M. Novaga - P. Pozzi

Anisotropic curvature flow of immersed networks

created by novaga on 04 Dec 2020
modified on 25 Jun 2021


Published Paper

Inserted: 4 dec 2020
Last Updated: 25 jun 2021

Journal: Milan J. Math.
Volume: 89
Number: 1
Pages: 147-186
Year: 2021

ArXiv: 2012.02490 PDF


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.