Opening nodes in the DPW method: co-planar case

TL;DR

This paper introduces a novel approach combining the DPW method and opening nodes to construct embedded constant mean curvature surfaces with Delaunay ends, regardless of genus or number of ends.

Contribution

It extends the DPW method by incorporating opening nodes to create more general embedded CMC surfaces with Delaunay ends.

Findings

Successfully constructs embedded CMC surfaces with arbitrary genus and ends.

Demonstrates the effectiveness of combining DPW and opening nodes techniques.

Provides new examples of CMC surfaces in Euclidean space.

Abstract

We combine the DPW method and opening nodes to construct embedded surfaces of positive constant mean curvature with Delaunay ends in euclidean space, with no limitation to the genus or number of ends.