Variational principles for circle patterns and Koebe's theorem
几何拓扑
2007-05-23 v2 复变函数
度量几何
摘要
We prove existence and uniqueness results for patterns of circles with prescribed intersection angles in constant curvature surfaces. Our method is based on two new functionals--one for the Euclidean and one for the hyperbolic case. We show how Colin de Verdi`ere's, Br"agger's and Rivin's functionals can be derived from ours.
关键词
引用
@article{arxiv.math/0203250,
title = {Variational principles for circle patterns and Koebe's theorem},
author = {Alexander I. Bobenko and Boris A. Springborn},
journal= {arXiv preprint arXiv:math/0203250},
year = {2007}
}
备注
33 pages, 12 figures, Appendix. Revised version. Appendix on cellular surfaces removed, references added and removed, typos corrected, a few minor changes