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arXiv · 1604.01284

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

Pietro Baldi·Emanuele Haus·Carlo Mantegazza
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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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Pietro Baldi, Emanuele Haus, Carlo Mantegazza. 2016-04-05. Non-Existence of Theta-Shaped Self-Similarly Shrinking Networks Moving by Curvature. https://arxiv.org/abs/1604.01284

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