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math.SP2025
On the heat content of compact quantum graphs
Patrizio Bifulco, Delio Mugnolo
We study the heat content for Laplacians on compact, finite metric graphs with Dirichlet conditions imposed at the "boundary" (i.e., a given set of vertices). We prove a closed for…
math.SP2025
Faber-Krahn inequality for the heat content on quantum graphs via random walk expansion
Patrizio Bifulco, Matthias Täufer
We study the heat content on quantum graphs and investigate whether an analogon of the Rayleigh-Faber-Krahn inequality holds. This means that heat content at time among graphs…
math.SP2025
Spectral comparison results for Laplacians on discrete graphs
Patrizio Bifulco, Joachim Kerner, Christian Rose
In the recent literature, various authors have studied spectral comparison results for Schrödinger operators with discrete spectrum in different settings including Euclidean domain…