2005/11/30 by Adrian Butscher, Frank Pacard, Butscher, Adrian +1
Engineering · Mathematics · Physics and Astronomy · #53Cxx #Advanced Differential Geometry Research #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.math/0511744
openalex publication_date 2005/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The (n+1)-sphere contains a simple family of constant mean curvature (CMC) hypersurfaces which are products of lower-dimensional spheres called the generalized Clifford hypersurfaces. This paper demonstrates that new, topologically non-trivial CMC hypersurfaces resembling a pair of neighbouring generalized Clifford tori connected to each other by small catenoidal bridges at a sufficiently symmetric configuration of points can be constructed by perturbative PDE methods. That is, one can create an approximate solution by gluing a rescaled catenoid into the neighbourhood of each point; and then one can show that a perturbation of this approximate hypersurface exists which satisfies the CMC condition. The results of this paper generalize those of the authors in math.DG/0511742.