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math.AP2025
Off-diagonal upper heat kernel bounds on graphs with unbounded geometry
Christian Rose
Results regarding off-diagonal Gaussian upper heat kernel bounds on discrete weighted graphs with possibly unbounded geometry are summarized and related. After reviewing uniform up…
math.AP2025
Optimal Poincaré-Hardy-type Inequalities on Manifolds and Graphs
Florian Fischer, Christian Rose
We review a method to obtain optimal Poincaré-Hardy-type inequalities on the hyperbolic spaces, and discuss briefly generalisations to certain classes of Riemannian manifolds. Afte…
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…