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

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

[BibTeX]

Published Paper

Inserted: 5 apr 2016
Last Updated: 16 jun 2018

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

Abstract:

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.