PreprintCC BY-NC-ND 4.0arXiv
Curvature Diffusion of Inverse-weight Lin--Lu--Yau Ricci Flow on Finite Trees
Abstract
We study the inverse-weight Lin--Lu--Yau Ricci flow on finite trees, and prove the convergence of the curvature on every edge via its diffusion equation. Moreover, the limiting curvature is the unique minimum-norm point of a polyhedron determined by the tree. We characterize possible limits of the normalized edge weights, give criteria for their convergence, and show that different positive initial metrics have equivalent omega-limit sets.
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BibTeX
@misc{bai2026curvature,
title = {{Curvature Diffusion of Inverse-weight Lin--Lu--Yau Ricci Flow on Finite Trees}},
author = {Shuliang Bai and Bobo Hua},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04671},
eprint = {2609.04671},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04671},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Curvature Diffusion of Inverse-weight Lin--Lu--Yau Ricci Flow on Finite Trees
AU - Shuliang Bai
AU - Bobo Hua
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.04671
UR - https://arxiv.org/abs/2609.04671
AB - We study the inverse-weight Lin--Lu--Yau Ricci flow on finite trees, and prove the convergence of the curvature on every edge via its diffusion equation. Moreover, the limiting curvature is the unique minimum-norm point of a polyhedron determined by the tree. We characterize possible limits of the normalized edge weights, give criteria for their convergence, and show that different positive initial metrics have equivalent omega-limit sets.
ER -