2014/10/13 by David Krieg, Krieg, David, Elías Wegert +2 · 1 citation
Engineering · Mathematics · #30C80 #30D40 #52C26 #Analytic and geometric function theory #Complex Variables (math.CV) #Elasticity and Wave Propagation #FOS: Mathematics #Holomorphic and Operator Theory #Metric Geometry (math.MG) #math.CV #math.MG #msc:30C80 #msc:30D40 #msc:52C26
paper · pdf · doi:10.48550/arxiv.1411.3228
38 pages, 22 figures. keywords: circle packing, crosscut, prime ends, conformal mapping, Schwarz's lemma, Apollonian packing
arxiv created 2014/10/13 · openalex publication_date 2014/10/13 · arxiv updated 2014/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.