Combinatorial p-th Calabi Flows and Fractional-order Calabi Flows for Generalized Hyperbolic Circle Packings

Abstract

This paper focuses on the generalized hyperbolic circle packings of finite polygonal cell decompositions with boundary values on surfaces with boundary. We investigate the problem of realizing generalized hyperbolic circle packings with given geodesic curvatures at bordered vertices and total geodesic curvatures at internal vertices and introduce the combinatorial p-th Calabi flows and the combinatorial fractional-order Calabi flows to find the desired generalized hyperbolic circle packings.

Keywords

Calabi flow / hyperbolic circle packings / total geodesic curvature / 52C25 / 52C26 / 57Q15

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Peking University