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arXiv · 2309.05215

A discrete uniformization theorem for decorated piecewise Euclidean metrics on surfaces

Xu Xu·Chao Zheng
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Abstract

In this paper, we introduce a new discretization of the Gaussian curvature on surfaces, which is defined as the quotient of the angle defect and the area of some dual cell of a weighted triangulation at the conic singularity. A discrete uniformization theorem for this discrete Gaussian curvature is established on surfaces with non-positive Euler number. The main tools are Bobenko-Lutz's discrete conformal theory for decorated piecewise Euclidean metrics on surfaces and variational principles with constraints.

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Xu Xu, Chao Zheng. 2023-09-11. A discrete uniformization theorem for decorated piecewise Euclidean metrics on surfaces. https://arxiv.org/abs/2309.05215

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