Constant mean curvature surfaces with Delaunay ends

1998/07/08 by Rafe Mazzeo, Frank Pacard, Mazzeo, Rafe +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #math.DG

paper · pdf · doi:10.48550/arxiv.math/9807039

arxiv created 1998/07/08 · openalex publication_date 1998/07/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a new class of complete constant mean curvature surfaces in R³. These are geometrically different than the surfaces constructed by Kapouleas' gluing technique. These are obtained by piecing together half-Delaunay surfaces to the truncations of minimal k-noids. The gluing techniques are new: the surfaces are obtained by matching Cauchy data from the infinite dimensional family of exact solutions of the problem on each of the component pieces. These surfaces are also proved to be nondegenerate in the CMC moduli space.

Citations

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

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