Constant mean curvature surfaces based on fundamental quadrilaterals

Alexander I. Bobenko, Sebastian Heller, Nicholas Schmitt

Published 2021-02-05Version 1

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.