Minimal surfaces of genus one with catenoidal ends II

Abstract

In the previous paper, we classified $n$-noids of genus one into two classes, and considered one of the classes. As a sequel, we give a necessary and sufficient condition for the existence of an $n$-noid of genus one with prescribed flux in the other class. By using the condition, we give obstructions for a certain type of flux and arrangement of the ends. We also give new examples by deforming a quadruple covering of Berglund--Rossman's $n$-end catenoid.