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arXiv · 2206.08550

Catenoid limits of singly periodic minimal surfaces with Scherk-type ends

Hao Chen·Peter Connor·Kevin Li
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Abstract

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.

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Hao Chen, Peter Connor, Kevin Li. 2022-06-17. Catenoid limits of singly periodic minimal surfaces with Scherk-type ends. https://doi.org/10.2140/pjm.2023.325.11

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