Geodesic nets on flat spheres
Differential Geometry
2025-04-30 v2
Abstract
We consider geodesic nets (critical points of a length functional on the space of embedded graphs) on doubled polygons (topological 2-spheres endowed with a flat metric away from finitely many cone singularities). We use the theorem of Gauss-Bonnet to demonstrate the existence and non-existence of specific geodesic nets on regular doubled polygons.
Keywords
Cite
@article{arxiv.2201.04761,
title = {Geodesic nets on flat spheres},
author = {Ian Adelstein and Elijah Fromm and Rajiv Nelakanti and Faren Roth and Supriya Weiss},
journal= {arXiv preprint arXiv:2201.04761},
year = {2025}
}