Embedded Constant Mean Curvature Surfaces in Euclidean Three Space

2012/10/11 by Christine Breiner, Breiner, Christine, Nikolaos Kapouleas +1
Mathematics · Physics and Astronomy · #53A10 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG #msc:53A10

paper · pdf · doi:10.48550/arxiv.1210.3394

6 figures

arxiv created 2012/10/11 · openalex publication_date 2012/10/11 · arxiv updated 2012/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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.

Citations

• The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation

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