Calculus of Variations and Geometric Measure Theory
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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

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Inserted: 5 apr 2016
Last Updated: 5 apr 2016

Year: 2016

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.


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