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Thomas Raujouan

Publications and source records attributed to Thomas Raujouan.

5 recordsLinked to original sources
arXiv2026

CmcMesh: a python implementation of the DPW method

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.

math.DG↗
arXiv2026

Constant curvature rotational nets and periodic Bäcklund transforms

After giving explicit parametrizations of discrete constant negative Gaussian curvature surfaces (negative CGC, i.e. discrete pseudospherical surfaces) of revolution, we construct Bäcklund transformations that again will have explicit parametrizations and are new examples of non-rotational discrete pseudospherical surfaces. In the process of doing this, for discrete CGC circular nets, we can provide rotationally invariant families of flat connections and give conditions on them so that the Bäcklund transformations preserve periodicity, that is, have annular topology.

math.DG↗
arXiv2024

Loop Weierstrass Representation

We introduce the Loop Weierstrass Representation for minimal surfaces in Euclidean space and constant mean curvature 1 surfaces in hyperbolic space by applying integral system methods to the Weierstrass and Bryant representations. We unify associated families, dual surfaces and Goursat transformations under the same holomorphic data, we introduce a simple factor dressing for minimal surfaces, and we compute and classify various examples.

math.DG↗
arXiv2019

On Delaunay Ends in the DPW Method

We consider constant mean curvature 1 surfaces in $\mathbb{R}^3$ arising via the DPW method from a holomorphic perturbation of the standard Delaunay potential on the punctured disk. Kilian, Rossman and Schmitt have proven that such a surface is asymptotic to a Delaunay surface. We consider families of such potentials parametrised by the necksize of the model Delaunay surface and prove the existence of a uniform disk on which the surfaces are close to the model Delaunay surface and are embedded in the unduloid case.

math.DG↗