Calculus of Variations and Geometric Measure Theory

P. Baldi - E. Haus - C. Mantegazza

Non-Existence of Theta-Shaped Self-Similarly Shrinking Networks Moving by Curvature

created by root on 05 Apr 2016
modified on 16 Jun 2018


Published Paper

Inserted: 5 apr 2016
Last Updated: 16 jun 2018

Journal: Comm. PDE
Volume: 43
Number: 3
Pages: 403-427
Year: 2018


We prove that there are no networks homeomorphic to the Greek ``theta'' letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees, such that under the motion by curvature they are self-similarly shrinking. This fact completes the classification of the self-similarly shrinking networks in the plane with at most two triple junctions.