English

Drawing cone spherical metrics via Strebel differentials

Complex Variables 2020-06-25 v2

Abstract

Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. By using Strebel differentials as a bridge, we construct a new class of cone spherical metrics on compact Riemann surfaces by drawing on the surfaces some class of connected metric ribbon graphs.

Keywords

Cite

@article{arxiv.1708.06535,
  title  = {Drawing cone spherical metrics via Strebel differentials},
  author = {Jijian Song and Yiran Cheng and Bo Li and Bin Xu},
  journal= {arXiv preprint arXiv:1708.06535},
  year   = {2020}
}

Comments

25 pages, 8 figures. Version 2: minor typo corrections; revised according to referee's comments. We substantially revised the proof of the second theorem to make its exposition easier to understand. We added a new section, where we discuss on the Riemann sphere the consistence of metrics generated by Strebel differentials with the two angle conditions by Mondello-Panov and Eremenko, respectively

R2 v1 2026-06-22T21:20:19.026Z