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math.SP2025
Spectral minimal partitions of unbounded domains
Matthias Hofmann, James B. Kennedy, Hugo Tavares
We study the problem of constructing -spectral minimal partitions of domains in dimensions, where the energy functional to be minimized is a -norm ()…
math.SP2025
On Courant-type bounds and spectral partitioning via Neumann domains on quantum graphs
Luís Baptista, Matthias Hofmann
We study the structure of eigenfunctions of the Laplacian on quantum graphs, with a particular focus on Morse eigenfunctions via nodal and Neumann domains. Building on Courant-type…
math.SP2025
On the asymptotic behavior of the spectral gap for discrete Schrödinger operators
Matthias Hofmann, Joachim Kerner, Maximilian Pechmann
In this note we elaborate on the asymptotic behavior of the spectral gap of a class of discrete Schrödinger operators defined on a path graph in the limit of infinite volume. We co…