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


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.

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