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arXiv · 2607.20986

CmcMesh: a python implementation of the DPW method

Thomas Raujouan·Martin Traizet
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Abstract

Minimal and constant mean curvature (CMC) surfaces in three-dimensional space forms can be constructed with the Dorfmeister--Pedit--Wu (DPW) method. We introduce CmcMesh, a Python implementation covering the whole pipeline from holomorphic potential to rendered surfaces, using Hoffman and Hoffman's Mesh algorithm. We implement the Weierstrass representation for minimal surfaces in $\mathbb{R}^3$, Bryant's representation for CMC-1 surfaces in $\mathbb{H}^3$, and the DPW method for CMC surfaces in $\mathbb{R}^3$ and for minimal and CMC surfaces in $\mathbb{S}^3$. The package is modular, making it easy to add new DPW variants without modifying existing code.

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Thomas Raujouan, Martin Traizet. 2026-07-23. CmcMesh: a python implementation of the DPW method. https://arxiv.org/abs/2607.20986

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