10 citations · 21 across the 3 of their papers we have counts for
16 papers
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…
Spectral gap of the largest eigenvalue of the normalized graph Laplacian
Jürgen Jost, Raffaella Mulas, Florentin Münch
We offer a new method for proving that the maximal eigenvalue of the normalized graph Laplacian of a graph with vertices is at least provided the graph is not…
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…
Large scale Ricci curvature on graphs
Mark Kempton, Gabor Lippner, Florentin Munch
We define a hybrid between Ollvier and Bakry Emery curvature on graphs with dependence on a variable neighborhood. The hexagonal lattice is non-negatively curved under this new cur…
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…