Geodesic nets on flat spheres
Ian Adelstein, Elijah Fromm, Rajiv Nelakanti, Faren Roth, Supriya, Weiss
TL;DR
This paper investigates the existence of geodesic nets on flat spheres formed by doubled polygons, applying Gauss-Bonnet theorem to determine when such nets exist or do not exist.
Contribution
It introduces a method to analyze geodesic nets on flat spheres with cone singularities, providing new existence and non-existence results for these structures.
Findings
Existence of geodesic nets on certain doubled polygons
Non-existence results for specific configurations
Application of Gauss-Bonnet theorem to flat spheres
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.
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Taxonomy
TopicsMorphological variations and asymmetry · Mathematical Dynamics and Fractals · advanced mathematical theories