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.

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

BALDI, PIETRO;HAUS, EMANUELE;MANTEGAZZA, Carlo Maria
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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/632362
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 2
social impact