46 citations · 133 across the 42 of their papers we have counts for
6 papers · 1 filter
Perpetual cutoff method and discrete Ricci curvature bounds with exceptions
Florentin Münch
One of the main obstacles regarding Barky Emery curvature on graphs is that the results require a global uniform lower curvature bounds where no exception sets are allowed. We over…
A discrete Hopf-Rinow-theorem
Matthias Keller, Florentin Münch
We prove a version of the Hopf-Rinow-theorem with respect to path metrics on discrete spaces. The novel aspect is that we do not a priori assume local finiteness but isolate a loca…
Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature
David Cushing, Supanat Kamtue, Jack Koolen +3
We introduce the notion of Bonnet-Myers and Lichnerowicz sharpness in the Ollivier Ricci curvature sense. Our main result is a classification of all self-centered Bonnet-Myers shar…
Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians
Matthias Keller, Florentin Münch
In this article, we prove gradient estimates under Bakry-Emery curvature bounds for unbounded graph Laplacians which satisfy an ellipticity assumption. As applications, we study co…
Coverings and the heat equation on graphs: stochastic incompleteness, the Feller property and uniform transience
Bobo Hua, Florentin Münch, Radosław K. Wojciechowski
We study regular coverings of graphs and manifolds with a focus on properties of the heat equation. In particular, we look at stochastic incompleteness, the Feller property and uni…
Curvature calculations for antitrees
David Cushing, Shiping Liu, Florentin Münch +1
In this article we prove that antitrees with suitable growth properties are examples of infinite graphs exhibiting strictly positive curvature in various contexts: in the normalize…