10 citations · 28 across the 9 of their papers we have counts for
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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…