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arXiv · 2509.22140

On the Ricci flow on Trees

Shuliang Bai·Bobo Hua·Yong Lin·Shuang Liu
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Abstract

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.

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Shuliang Bai, Bobo Hua, Yong Lin, Shuang Liu. 2026-01-28. On the Ricci flow on Trees. https://arxiv.org/abs/2509.22140

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