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arXiv · 1604.06440

An end-to-end construction of doubly periodic minimal surfaces

Peter Connor·Kevin Li
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Abstract

Using Traizet's regeneration method, we prove that for each positive integer n there is a family of embedded, doubly periodic minimal surfaces with parallel ends in Euclidean space of genus 2n-1 and 4 ends in the quotient by the maximal group of translations. The genus 2n-1 family converges smoothly to 2n copies of Scherk's doubly periodic minimal surface. The only previously known doubly periodic minimal surfaces with parallel ends and genus greater than 3 limit in a foliation of Euclidean space by parallel planes.

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Peter Connor, Kevin Li. 2016-04-21. An end-to-end construction of doubly periodic minimal surfaces. https://arxiv.org/abs/1604.06440

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