The Calabi flow with prescribed curvature on finite graphs
Differential Geometry
2026-04-06 v1
Abstract
In this paper, we investigate the prescribed curvature problem associated with a special Lin-Lu-Yau curvature on finite graphs of girth at least 6. We define the corresponding Calabi flow for this curvature type, and establish an equivalent characterization of the problem, namely, the solution to the Calabi flow exists globally in time and converges if and only if there exists a weight function that realizes the prescribed curvature. In particular, for constant curvature weights, we prove that the solution to the Calabi flow exists globally in time and converges under certain topological conditions.
Keywords
Cite
@article{arxiv.2604.02632,
title = {The Calabi flow with prescribed curvature on finite graphs},
author = {Yi Li and Jie Wang and Pingsan Yuan and Chao Zheng},
journal= {arXiv preprint arXiv:2604.02632},
year = {2026}
}