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Geodesic nets
on flat spheres
Ian Adelstein, Elijah Fromm, Rajiv Nelakanti, Faren Roth and Supriya Weiss |
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Vol. 18 (2025), No. 3, 539–546
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Abstract |
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We consider geodesic nets (critical points of a length functional on the space of embedded graphs) on doubled polygons (topological -spheres endowed with a flat metric away from finitely many cone singularities). We use the theorem of Gauss–Bonnet to demonstrate the existence and nonexistence of specific geodesic nets on regular doubled polygons. |
Keywords
geodesic nets, flat spheres, doubled polygons, Gauss–Bonnet
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Mathematical Subject Classification
Primary: 53C22, 53C23
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Milestones
Received: 20 September 2023
Revised: 30 November 2023
Accepted: 3 December 2023
Published: 28 April 2025
Communicated by Frank Morgan
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Authors |
| Ian Adelstein | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Elijah Fromm | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Rajiv Nelakanti | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Faren Roth | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Supriya Weiss | |
| Department of Mathematics Yale University New Haven, CT United States |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
