2 papers
math.SP2025
Geodesic nets via eigenvalue optimisation
Duc Hoang Cao
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{…
math.SP2025
Eigenvalue bounds for Schrödinger operators on quantum graphs with -coupling conditions
Duc Hoang Cao
We prove sharp upper bounds for eigenvalues of Schrödinger operators on quantum graphs with -coupling (also known as Robin) conditions at all vertices. The bounds depend on th…