论文标题
属于$ \ mathbb {h}^2 \ times \ mathbb {r} $中的最小k-noids和鞍塔
Genus one minimal k-noids and saddle towers in $\mathbb{H}^2\times\mathbb{R}$
论文作者
论文摘要
对于每个$ k \ geq 3 $，我们在Riemannian Product Space $ \ Mathbb {h}^2 \ times \ times \ times \ Mathbb {r} $中构建了一个完整的Alexandrov abbedded minimal表面的1-参数家族。我们还以$ \ mathbb {h}^2 \ times \ times \ mathbb {r} $的方式获得了$ 1 $ $ 1 $和$ 2K $的完整最小表面。他们都相对于$ k $垂直飞机以及有限的总曲率$-4Kπ$具有二面性对称性。最后，我们还提供了完全正确的Alexandrov插入的最小表面的示例，具有有限的总曲率，$ 1 $ 1 $ 1 $ $ \ MATHBB {h}^2 \ times \ times \ times \ times \ times \ mathbb {r} $通过多皮子或寄生虫翻译的作用。
For each $k\geq 3$, we construct a 1-parameter family of complete properly Alexandrov-embedded minimal surfaces in the Riemannian product space $\mathbb{H}^2\times\mathbb{R}$ with genus $1$ and $k$ embedded ends asymptotic to vertical planes. We also obtain complete minimal surfaces with genus $1$ and $2k$ ends in the quotient of $\mathbb{H}^2\times\mathbb{R}$ by an arbitrary vertical translation. They all have dihedral symmetry with respect to $k$ vertical planes, as well as finite total curvature $-4kπ$. Finally, we also provide examples of complete properly Alexandrov-embedded minimal surfaces with finite total curvature with genus $1$ in quotients of $\mathbb{H}^2\times\mathbb{R}$ by the action of a hyperbolic or parabolic translation.
