Rigidity of Circle Packings with Crosscuts
Complex Variables
2014-11-13 v1 Metric Geometry
Abstract
Circle packings with specified patterns of tangencies form a discrete counterpart of analytic functions. In this paper we study univalent packings (with a combinatorial closed disk as tangent graph) which are embedded in (or fill) a bounded, simply connected domain. We introduce the concept of crosscuts and investigate the rigidity of circle packings with respect to maximal crosscuts. The main result is a discrete version of an indentity theorem for analytic functions (in the spirit of Schwarz' Lemma), which has implications to uniqueness statements for discrete conformal mappings.
Cite
@article{arxiv.1411.3228,
title = {Rigidity of Circle Packings with Crosscuts},
author = {David Krieg and Elias Wegert},
journal= {arXiv preprint arXiv:1411.3228},
year = {2014}
}
Comments
38 pages, 22 figures. keywords: circle packing, crosscut, prime ends, conformal mapping, Schwarz's lemma, Apollonian packing