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arXiv · 2210.00514

Graphs with nonnegative curvature outside a finite subset, harmonic functions and number of ends

Bobo Hua·Florentin Münch
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Abstract

We study graphs with nonnegative Bakry-\'Emery curvature or Ollivier curvature outside a finite subset. For such a graph, via introducing the discrete Gromov-Hausdorff convergence we prove that the space of bounded harmonic functions is finite dimensional, and as a corollary the number of non-parabolic ends is finite.

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Bobo Hua, Florentin Münch. 2022-10-02. Graphs with nonnegative curvature outside a finite subset, harmonic functions and number of ends. https://arxiv.org/abs/2210.00514

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