Circle patterns on surfaces of finite topological type
Huabin Ge, Bobo Hua, Ze Zhou
Abstract
This paper investigates circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. We characterise the images of the curvature maps and establish several equivalent conditions regarding long time behaviors of Chow-Luo's combinatorial Ricci flows for these patterns. As consequences, several generalizations of circle pattern theorem are obtained. Moreover, our approach suggests a computational method to find the desired circle patterns.
Topics & Concepts
MathematicsType (biology)Intersection (aeronautics)CurvatureTopology (electrical circuits)Circle packingPure mathematicsIntersection theorySurface (topology)GeometryCombinatoricsMathematical analysisBiologyEngineeringOrdinary differential equationDifferential equationDifferential algebraic equationAerospace engineeringEcologyMathematical Dynamics and FractalsTopological and Geometric Data AnalysisGeometric Analysis and Curvature Flows