2000 character limit reached
Geodesic nets via eigenvalue optimisation (2508.16331v1)
Published 22 Aug 2025 in math.SP and math.DG
Abstract: We explore a connection between geodesic nets and quantum graphs optimising certain functionals from spectral theory. For surfaces, critical metrics for the normalised $k{\mathrm{th}}$ eigenvalue of the Laplacian give rise to isometric minimal immersions to a unit sphere. In this spirit we obtain geodesic nets from optimal quantum graphs, and obstructions to the existence of critical metrics.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.