The Ideal Circle Pattern with Boundaries via Analytic Method

Abstract

The geometric structure of three-dimensional manifolds is a fundamental problem in geometric topology. In this paper, we investigate the ideal circle pattern problem on a surface with boundaries under a cellular decomposition. Employing the variational method, we establish a series of equivalent conditions for the existence of a circle pattern in both Euclidean and hyperbolic background geometries.

Keywords

Ideal circle pattern / analytic method / generalized Gaussian curvature

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Peking University