On the Ricci flow on Trees
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908792913920000 |
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| author | Bai, Shuliang Hua, Bobo Lin, Yong Liu, Shuang |
| author_facet | Bai, Shuliang Hua, Bobo Lin, Yong Liu, Shuang |
| contents | In this paper, we study the evolution of metrics on finite trees under continuous-time Ricci flows based on the Lin-Lu-Yau version of Ollivier Ricci curvature. We analyze long-time dynamics of edge weights and curvatures, providing precise characterizations of their limiting behaviors. We prove that the Ricci flow converges to metric with zero curvature on edges whose normalized weights converge to positive values only if the tree is a caterpillar tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22140 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Ricci flow on Trees Bai, Shuliang Hua, Bobo Lin, Yong Liu, Shuang Differential Geometry 53C21 In this paper, we study the evolution of metrics on finite trees under continuous-time Ricci flows based on the Lin-Lu-Yau version of Ollivier Ricci curvature. We analyze long-time dynamics of edge weights and curvatures, providing precise characterizations of their limiting behaviors. We prove that the Ricci flow converges to metric with zero curvature on edges whose normalized weights converge to positive values only if the tree is a caterpillar tree. |
| title | On the Ricci flow on Trees |
| topic | Differential Geometry 53C21 |
| url | https://arxiv.org/abs/2509.22140 |