46 citations · 133 across the 42 of their papers we have counts for
25 papers · 1 filter
Transitive graphs of non-negative Ollivier-Ricci curvature have polynomial growth
Camillo Brena, Tom Hutchcroft, Florentin Münch
We prove that every transitive graph of non-negative Ollivier-Ricci curvature has polynomial growth. We deduce from this and a theorem of Brena and Brue that a finitely generated g…
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…
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…
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 the -…
Cheeger type inequalities associated with isocapacitary constants on graphs
Bobo Hua, Florentin Münch, Tao Wang
In this paper, we introduce Cheeger type constants via isocapacitary constants introduced by Maz'ya to estimate first Dirichlet, Neumann and Steklov eigenvalues on a finite subgrap…
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-M…
Bakry-Émery calculus for entropic curvature, new diameter estimates, and spectral gaps
Supanat Kamtue, Shiping Liu, Florentin Münch +1
In this paper, we propose a generalization of Bakry-Émery's calculus which allows us to formulate both Bakry-Émery and entropic curvature simultaneously. This formulation represent…
Ollivier curvature, Isoperimetry, concentration, and Log-Sobolev inequalitiy
Florentin Münch
We introduce a Laplacian separation principle for the the eikonal equation on Markov chains. As application, we prove an isoperimetric concentration inequality for Markov chains wi…
Some variants of discrete positive mass theorems on graphs
Bobo Hua, Florentin Münch, Haohang Zhang
Inspired by asymptotically flat manifolds, we introduce the concept of asymptotically flat graphs and define the discrete ADM mass on them. We formulate the discrete positive mass…
Graphs with nonnegative curvature outside a finite subset, harmonic functions and number of ends
Bobo Hua, Florentin Münch
We study graphs with nonnegative Bakry-Émery curvature or Ollivier curvature outside a finite subset. For such a graph, via introducing the discrete Gromov-Hausdorff convergence we…
Characterizations of Forman curvature
Jürgen Jost, Florentin Münch
We characterize Forman curvature lower bounds via contractivity of the Hodge Laplacian semigroup. We prove that Ollivier and Forman curvature coincide on edges when maximizing the…
Every Salami has two ends
Bobo Hua, Florentin Münch
A salami is a connected, locally finite, weighted graph with non-negative Ollivier Ricci curvature and at least two ends of infinite volume. We show that every salami has exactly t…
Spectrally positive Bakry-Émery Ricci curvature on graphs
Florentin Münch, Christian Rose
We investigate analytic and geometric implications of non-constant Ricci curvature bounds. We prove a Lichnerowicz eigenvalue estimate and finiteness of the fundamental group assum…
Li-Yau inequality under on graphs
Florentin Münch
We introduce a modified non-linear heat equation as a substitute of where is the heat semigroup. We prove an exponential decay of u…
Non-negative Ollivier curvature on graphs, reverse Poincaré inequality, Buser inequality, Liouville property, Harnack inequality and eigenvalue estimates
Florentin Münch
We prove that for combinatorial graphs with non-negative Ollivier curvature, one has \[ \|P_t μ- P_t ν\|_1 \leq \frac{W_1(μ,ν)}{\sqrt{t}} \] for all probability measures wher…
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…
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…
Ricci curvature on birth-death processes
Bobo Hua, Florentin Münch
In this paper, we study curvature dimension conditions on birth-death processes which correspond to linear graphs, i.e., weighted graphs supported on the infinite line or the half…
Ollivier Ricci curvature for general graph Laplacians: Heat equation, Laplacian comparison, non-explosion and diameter bounds
Florentin Münch, Radoslaw K. Wojciechowski
Discrete time random walks on a finite set naturally translate via a one-to-one correspondence to discrete Laplace operators. Typically, Ollivier curvature has been investigated vi…
Rigidity properties of the hypercube via Bakry-Emery curvature
Shiping Liu, Florentin Münch, Norbert Peyerimhoff
We give rigidity results for the discrete Bonnet-Myers diameter bound and the Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a…
Distance bounds for graphs with some negative Bakry-Émery curvature
Shiping Liu, Florentin Münch, Norbert Peyerimhoff +1
We prove distance bounds for graphs possessing positive Bakry-Émery curvature apart from an exceptional set, where the curvature is allowed to be non-positive. If the set of non-po…
Ricci curvature and eigenvalue estimates for the magnetic Laplacian on manifolds
Michela Egidi, Shiping Liu, Florentin Münch +1
In this paper, we present a Lichnerowicz type estimate and (higher order) Buser type estimates for the magnetic Laplacian on a closed Riemannian manifold with a magnetic potential.…
Bakry-Emery curvature and diameter bounds on graphs
Shiping Liu, Florentin Münch, Norbert Peyerimhoff
We prove diameter bounds for graphs having positive Ricci-curvature bound in Bakry-Emery sense. One result using only curvature and maximal vertex degree is sharp in case of hyperc…
Remarks on curvature dimension conditions on graphs
Florentin Münch
We show a connection between the inequality and the inequality. In particular, we introduce a inequality as a slight generalization of which turns out t…