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Geodesic nets via eigenvalue optimisation

Published 22 Aug 2025 in math.SP and math.DG | (2508.16331v1)

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.

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Authors (1)

  1. Duc Hoang Cao 

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