Geometric Data for Triply Periodic Minimal Surfaces in Spaces of Constant Curvature

in: Geometric Analysis and Computer Graphics, P. Concus, D. Hoffman, R. Finn (Eds.) 1991.

Konrad Polthier

Abstract

In this note we describe the use of geometric data for the construction of triply periodic minimal surfaces in R³, S³, and H³. With a conjugate surface construction we obtain the Plateau solution of a fundamental piece for the symmetry group of the minimal surface. For some examples in R³ a method of H. Karcher and M. Wohlgemuth has led to the Weierstraß formula.

Full Preprint: (--)