The Singly Periodic Genus-One Helicoid
微分几何
2016-09-06 v1
摘要
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: rotation about the vertical line; rotation about the horizontal lines (the same symmetry); and their composition.
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引用
@article{arxiv.math/9605222,
title = {The Singly Periodic Genus-One Helicoid},
author = {David Hoffman and Hermann Karcher and Fusheng Wei},
journal= {arXiv preprint arXiv:math/9605222},
year = {2016}
}