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We consider a network in the Euclidean plane that consists of three distinct half-lines with common start points. From that network as initial condition, there exists a network that consists of three curves that all start at one point, where they form degree angles, and expands homothetically under curve shortening flow. We also prove uniqueness of these networks.
@article{ASNSP_2007_5_6_4_511_0,
author = {Schn\"urer, Oliver C. and Schulze, Felix},
title = {Self-similarly expanding networks to curve shortening flow},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {511--528},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 6},
number = {4},
year = {2007},
mrnumber = {2394409},
zbl = {1139.53031},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_4_511_0/}
}
TY - JOUR AU - Schnürer, Oliver C. AU - Schulze, Felix TI - Self-similarly expanding networks to curve shortening flow JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2007 SP - 511 EP - 528 VL - 6 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_4_511_0/ LA - en ID - ASNSP_2007_5_6_4_511_0 ER -
%0 Journal Article %A Schnürer, Oliver C. %A Schulze, Felix %T Self-similarly expanding networks to curve shortening flow %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2007 %P 511-528 %V 6 %N 4 %I Scuola Normale Superiore, Pisa %U http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_4_511_0/ %G en %F ASNSP_2007_5_6_4_511_0
Schnürer, Oliver C.; Schulze, Felix. Self-similarly expanding networks to curve shortening flow. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 4, pp. 511-528. http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_4_511_0/