Combinatorial Calabi flow for ideal circle pattern
Differential Geometry
2025-04-16 v2 Complex Variables
Abstract
We study the combinatorial Calabi flow for ideal circle patterns in both hyperbolic and Euclidean background geometry. We prove that the flow exists for all time and converges exponentially fast to an ideal circle pattern metric on surfaces with prescribed attainable curvatures. As a consequence, we provide an algorithm to find the desired ideal circle patterns.
Cite
@article{arxiv.2501.01678,
title = {Combinatorial Calabi flow for ideal circle pattern},
author = {Shengyu Li and Zhigang Wang},
journal= {arXiv preprint arXiv:2501.01678},
year = {2025}
}
Comments
14 pages,2 figures