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math.DG2019
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…
math.DG2019★ 1 cited
Almost positive Ricci curvature in Kato sense -- an extension of Myers' theorem
Christian Rose
It is shown that if the Kato constant of the negative part of the Ricci curvature below a positive level is small, then the volume of the corresponding manifold can be bounded abov…
math.DG2019★ 6 cited
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…