论文标题
用Scherk型末端的单一周期性最小表面的链球化极限
Catenoid limits of singly periodic minimal surfaces with Scherk-type ends
论文作者
论文摘要
我们建立了任何商$ g $的嵌入式，单一的周期性最小表面，任何偶数$ 2n> 2 $ 2n> 2 $几乎平行的Scherk终点。这样一个家庭中的表面看起来像是$ n $平行的飞机，由$ n-1+g $小的catenoid颈部连接。在限制下，该家庭收敛到$ n $表的垂直平面，其中$ n-1+g $ sickular点被称为商中的节点。为了使节点开放到链球菌颈部，它们的位置必须满足一组平衡方程，其解决方案由stieltjes多项式的根部给出。
We construct families of embedded, singly periodic minimal surfaces of any genus $g$ in the quotient with any even number $2n>2$ of almost parallel Scherk ends. A surface in such a family looks like $n$ parallel planes connected by $n-1+g$ small catenoid necks. In the limit, the family converges to an $n$-sheeted vertical plane with $n-1+g$ singular points termed nodes in the quotient. For the nodes to open up into catenoid necks, their locations must satisfy a set of balance equations whose solutions are given by the roots of Stieltjes polynomials.
