Self-intersecting three-periodic minimal surfaces forming two-periodic (flat) labyrinths

Abstract

14 families of minimal surfaces with straight self-intersections have been derived which subdivide R 3 into infinitely many congruent, two-periodic`flat labyrinths'. For eleven families, all flat labyrinths are parallel to each other. Two sets of mutual perpendicular flat labyrinths have been found three times. All these minimal surfaces are non-orientable. Their Euler characteristics vary between À3 and À13.