1996/05/17 by David Hoffman, Hermann Karcher, Hoffman, David +3
Computer Science · Materials Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Quasicrystal Structures and Properties #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.math/9605222
We prove the existence of a complete, embedded, singly periodic minimal surface, whose quotient by vertical translations has genus one and two ends. The existence of this surface was announced in our paper in \it Bulletin of the AMS, 29(1):77--84, 1993. Its ends in the quotient are asymptotic to one full turn of the helicoid, and, like the helicoid, it contains a vertical line. Modulo vertical translations, it has two parallel horizontal lines crossing the vertical axis. The nontrivial symmetries of the surface, modulo vertical translations, consist of: 180^∘ rotation about the vertical line; 180^∘ rotation about the horizontal lines (the same symmetry); and their composition.