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The notions of discrete conformality on triangle meshes have richmathematical theories and wide applications. The related notions of discreteuniformizations on triangle meshes, suggest efficient methods for computing theuniformizations of surfaces. This paper proves that the discreteuniformizations approximate the continuous uniformization for closed surfacesof genus $\geq1$, when the approximating triangle meshes are reasonably good.To the best of the authors' knowledge, this is the first convergence result oncomputing uniformizations for surfaces of genus $>1$.

The Convergence of Discrete Uniformizations for Closed Surfaces