单周期亏格一螺旋面
The Singly Periodic Genus-One Helicoid
摘要：
本文证明了一个完备的、嵌入的、单周期的极小曲面的存在性，它的垂直平移商具有亏格一和两端。我们在{ \it Bulletin of the AMS}，29（1）：77- 84，1993中的论文中宣布了这种表面的存在。它在商中的端点渐近于螺旋面的一整圈，并且像螺旋面一样，它包含一条垂直线。模垂直平移，它有两条平行的水平线穿过垂直轴。非平凡的对称性的表面，模垂直平移，包括：$180^\circ$旋转的垂直线; $180^\circ$旋转的水平线（相同的对称性）;和他们的组成。
英文摘要：
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: $180^\circ$ rotation about the vertical line; $180^\circ$ rotation about the horizontal lines (the same symmetry); and their composition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
