Opening nodes and the DPW method

TL;DR

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

Contribution

It presents a new technique that removes previous limitations on genus and number of ends in constructing such surfaces.

Findings

Successfully constructs embedded CMC surfaces with arbitrary genus and ends.

Extends the applicability of the DPW method in geometric analysis.

Provides explicit examples of new CMC surfaces.

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.