7 papers · 1 filter
Bounded-degree graphs of non-negative Ollivier-Ricci curvature have subexponential growth and diffusive random walk
Tom Hutchcroft, Florentin Münch
We study the geometric properties of graphs with non-negative Ollivier-Ricci curvature, a discrete analogue of non-negative Ricci curvature in Riemannian geometry. We prove that fo…
A generalized Cheeger inequality and the Steklov Problem on finite graphs
Bobo Hua, Supanat Kamtue, Shiping Liu +2
We prove generalized Cheeger inequalities for eigenvalues of Laplacians for reversible Markov chains. Then we apply Hassannezhad and Miclo's convergence result to obtain Jammes Che…
Inequalities between Dirichlet and Neumann Eigenvalues on Surfaces
Bobo Hua, Florentin Münch, Haohang Zhang
For a bounded Lipschitz domain in a Riemannian surface satisfying certain curvature condition, we prove that where ( resp.) is th…
A counterexample to a conjecture by Salez and Youssef
Florentin Münch
Remarkable progress has been made in recent years to establish log-Sobolev type inequalities under the assumption of discrete Ricci curvature bounds. More specfically, Salez and Yo…
Liouville property and non-negative Ollivier curvature on graphs
Jürgen Jost, Florentin Münch, Christian Rose
For graphs with non-negative Ollivier curvature, we prove the Liouville property, i.e., every bounded harmonic function is constant. Moreover, we improve Ollivier's results on conc…
Entropic curvature not comparable to other curvatures -- or is it?
Supanat Kamtue, Shiping Liu, Florentin Münch +1
In this paper we consider global -curvatures of finite Markov chains with associated means in the spirit of the entropic curvature (based on the logarithmic mean) by Erbar…