New explicit CMC cylinders and same-lobed CMC multibubbletons

TL;DR

This paper introduces explicit parametrizations of Darboux transforms of Delaunay surfaces, leading to new closed constant mean curvature (CMC) surfaces with dihedral symmetry and the construction of same-lobed CMC multibubbletons.

Contribution

It provides explicit formulas for Darboux transforms of Delaunay surfaces and constructs new closed CMC multibubbletons with dihedral symmetry using Bianchi permutability.

Findings

Explicit parametrizations of Darboux transforms of Delaunay surfaces

New closed CMC surfaces with dihedral symmetry

Construction of same-lobed CMC multibubbletons

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.