New explicit CMC cylinders and same-lobed CMC multibubbletons

2022/05/29 by Joseph Cho, Cho, Joseph, Katrin Leschke +3
Computer Science · Engineering · Mathematics · #(2020): 53A10 (Primary) 37K35 #58E20 (Secondary) #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2205.14675

openalex publication_date 2022/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide explicit parametrisations of all Darboux transforms of Delaunay surfaces. Using the Darboux transformation on a multiple cover, we obtain this way new closed CMC surfaces with dihedral symmetry. These can be used to construct closed same-lobed CMC multibubbletons by applying Bianchi permutability.

Related

• Realizing pairs of multicurves as cylinders on translation surfaces
• Minimal Darboux transformations
• Discrete surfaces of constant mean curvature via dressing
• Exploring the space of compact symmetric CMC surfaces
• Constant mean curvature surfaces with Delaunay ends