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Curvature flow in conformal mapping. (English) Zbl 1073.52511
Summary: We use a simple example to introduce a notion of curvature flow in the conformal mapping of polyhedral surfaces. The inquiry was motivated by experiments with discrete conformal maps in the sense of circle packing. We describe the classical theory behind these flows and demonstrate how to modify the Schwarz-Christoffel method to obtain classical numerical confirmation. We close with some additional examples.

MSC:
52C26 Circle packings and discrete conformal geometry
30C30 Schwarz-Christoffel-type mappings
53A30 Conformal differential geometry (MSC2010)
65D15 Algorithms for approximation of functions
37E35 Flows on surfaces
53A05 Surfaces in Euclidean and related spaces
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