An end-to-end-construction for singly periodic minimal surfaces

TL;DR

This paper demonstrates the construction of new singly periodic minimal surfaces in three-dimensional space with arbitrary genus and Scherk type ends, using a gluing method of known minimal surface pieces.

Contribution

It introduces an end-to-end construction method for creating a wide variety of singly periodic minimal surfaces with specified topological and geometric features.

Findings

Existence of new families of singly periodic minimal surfaces.

Construction method based on gluing known minimal surface pieces.

Surfaces have finite genus and Scherk type ends.

Abstract

We show the existence of various families of properly embedded singly periodic minimal surfaces in R^3 with finite arbitrary genus and Scherk type ends in the quotient. The proof of our results is based on the gluing of small perturbations of pieces of already known minimal surfaces.