English

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.

Keywords

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

R2 v1 2026-06-28T20:55:16.252Z