On the Ricci flow on Trees
Differential Geometry
2026-01-29 v3
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.
Cite
@article{arxiv.2509.22140,
title = {On the Ricci flow on Trees},
author = {Shuliang Bai and Bobo Hua and Yong Lin and Shuang Liu},
journal= {arXiv preprint arXiv:2509.22140},
year = {2026}
}
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