On the Classification of Networks Self–Similarly Moving by Curvature

Pietro Baldi, Emanuele Haus, and Carlo Mantegazza. "On the Classification of Networks Self–Similarly Moving by Curvature." Geometric Flows 2.1 (2017): null. <http://eudml.org/doc/288500>.

@article{PietroBaldi2017,
abstract = {We give an overview of the classification of networks in the plane with at most two triple junctions with the property that under the motion by curvature they are self-similarly shrinking. After the contributions in [7, 9, 20], such a classification was completed in the recent work in [4] (see also [3]), proving that there are no self-shrinking networks homeomorphic to the Greek “theta” letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees. We present the main geometric ideas behind the work [4]. We also briefly introduce our work in progress in the higher-dimensional case of networks of surfaces in R3.},
author = {Pietro Baldi, Emanuele Haus, Carlo Mantegazza},
journal = {Geometric Flows},
language = {eng},
number = {1},
pages = {null},
title = {On the Classification of Networks Self–Similarly Moving by Curvature},
url = {http://eudml.org/doc/288500},
volume = {2},
year = {2017},
}

TY - JOUR
AU - Pietro Baldi
AU - Emanuele Haus
AU - Carlo Mantegazza
TI - On the Classification of Networks Self–Similarly Moving by Curvature
JO - Geometric Flows
PY - 2017
VL - 2
IS - 1
SP - null
AB - We give an overview of the classification of networks in the plane with at most two triple junctions with the property that under the motion by curvature they are self-similarly shrinking. After the contributions in [7, 9, 20], such a classification was completed in the recent work in [4] (see also [3]), proving that there are no self-shrinking networks homeomorphic to the Greek “theta” letter (a double cell) embedded in the plane with two triple junctions with angles of 120 degrees. We present the main geometric ideas behind the work [4]. We also briefly introduce our work in progress in the higher-dimensional case of networks of surfaces in R3.
LA - eng
UR - http://eudml.org/doc/288500
ER -