Liouville property and non-negative Ollivier curvature on graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
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| _version_ | 1866913773297598464 |
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| author | Jost, Jürgen Münch, Florentin Rose, Christian |
| author_facet | Jost, Jürgen Münch, Florentin Rose, Christian |
| contents | 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 concentration of the measure under positive Ollivier curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_10796 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Liouville property and non-negative Ollivier curvature on graphs Jost, Jürgen Münch, Florentin Rose, Christian Differential Geometry 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 concentration of the measure under positive Ollivier curvature. |
| title | Liouville property and non-negative Ollivier curvature on graphs |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1903.10796 |