English

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}
}