3 papers
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.AP2024
Gaussian upper heat kernel bounds and Faber-Krahn inequalities on graphs
Christian Rose
We investigate the equivalence of relative Faber-Krahn inequalities and the conjunction of Gaussian upper heat kernel bounds and volume doubling on large scales on graphs. For the…