English

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

Differential Geometry 2022-10-04 v1

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.

Keywords

Cite

@article{arxiv.2210.00514,
  title  = {Graphs with nonnegative curvature outside a finite subset, harmonic functions and number of ends},
  author = {Bobo Hua and Florentin Münch},
  journal= {arXiv preprint arXiv:2210.00514},
  year   = {2022}
}