Royal Society Publishing

Spanning Minimal Surfaces

W. Fischer , E. Koch

Abstract

Spanning minimal surfaces are 3-periodic minimal surfaces which contain straight lines, i.e. axes of 2-fold symmetry. We have used crystallographic knowledge of the space groups and of the corresponding arrangements of 2-fold axes involved for the derivation of new surfaces of this type and for their systematic description. Complete information on spanning minimal surfaces without self-intersections is given with respect to their symmetry and topology, together with some new results on spanning minimal surfaces with self-intersections along straight lines.

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