Constant mean curvature surfaces based on fundamental quadrilaterals

Abstract

We describe the construction of CMC surfaces with symmetries in ${\mathbb{S}}^3$ and ${\mathbb{R}}^3$ using a CMC quadrilateral in a fundamental tetrahedron of a tessellation of the space. The fundamental piece is constructed by the generalized Weierstrass representation using a geometric flow on the space of potentials.

22 pages, 30 figures

References in corpus (1)

• DPW Potentials for Compact Symmetric CMC Surfaces in ${\mathbb{S}}^3$

Cited by in corpus (1)

• Conjugate Plateau constructions in product spaces