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Geodesic nets on flat spheres
Published 13 Jan 2022 in math.DG | (2201.04761v2)
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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