A Gluing Construction for Prescribed Mean Curvature

2009/02/20 by Adrian Butscher, Butscher, Adrian
Engineering · Mathematics · #53Cxx #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:53Cxx

paper · pdf · doi:10.48550/arxiv.0902.3499

10 pages

arxiv created 2009/02/20 · openalex publication_date 2009/02/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end along a line segment. The condition on the existence of these hypersurfaces is the vanishing of the sum of certain integral moments of the spheres with respect the prescribed mean curvature function.

Related

• Constant Mean Curvature Hypersurfaces in the (n+1)-Sphere by Gluing Spherical Building Blocks
• Constant Mean Curvature Hypersurfaces Condensing to Geodesic Segments and Rays in Riemannian Manifolds
• Gluing Constructions Amongst Constant Mean Curvature Hypersurfaces in the (n+1)-Sphere
• Constant Mean Curvature surfaces with prescribed finite topologies
• Connected sums of constant mean curvature surfaces in Euclidean 3 space