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, see [5, 10, 25, 2].
Baldi, P., Haus, E., Mantegazza, C. (2018). Non–existence of theta–shaped self–similarly shrinking networks moving by curvature. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 43(3), 403-427 [10.1080/03605302.2018.1446162].
Non–existence of theta–shaped self–similarly shrinking networks moving by curvature
Baldi, Pietro;Haus, Emanuele;Mantegazza, Carlo
2018-01-01
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, see [5, 10, 25, 2].File in questo prodotto:
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