Embedded Constant Mean Curvature Surfaces in Euclidean Three Space

TL;DR

This paper refines the construction of complete constant mean curvature surfaces in Euclidean 3-space, enabling the creation of many new embedded examples with finite topology by improving previous methodologies.

Contribution

It introduces a more precise methodology that removes previous restrictions, allowing for the construction of a broader class of embedded constant mean curvature surfaces.

Findings

Removed severe restrictions on embeddedness

Produced a large class of new embedded examples

Enhanced the construction methodology

Abstract

In this paper we refine the construction and related estimates for complete Constant Mean Curvature surfaces in Euclidean three-space developed in Kapouleas (1990) by adopting the more precise and powerful version of the methodology which was developed in Kapouleas (1995). As a consequence we remove the severe restrictions in establishing embeddedness for complete Constant Mean Curvature surfaces in Kapouleas (1990) and we produce a very large class of new embedded examples of finite topology.