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arXiv · 2201.04761

Geodesic nets on flat spheres

Ian Adelstein·Elijah Fromm·Rajiv Nelakanti·Faren Roth·Supriya Weiss
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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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Ian Adelstein, Elijah Fromm, Rajiv Nelakanti, Faren Roth, Supriya Weiss. 2022-01-13. Geodesic nets on flat spheres. https://doi.org/10.2140/involve.2025.18.539

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