Generalized Doubling Constructions for Constant Mean Curvature Hypersurfaces in the (n+1)-Sphere
| dc.creator | Butscher, Adrian | |
| dc.creator | Pacard, Frank | |
| dc.date | 2005-11-30 | |
| dc.date | 2006-12-23 | |
| dc.date.accessioned | 2026-07-07T07:36:58Z | |
| dc.date.available | 2026-07-07T07:36:58Z | |
| dc.description | 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. | |
| dc.description | 18 pages. Final revised version accepted for publication in Annals of Global Analysis and Geometry | |
| dc.identifier | https://arxiv.org/abs/math/0511744 | |
| dc.identifier | http://arxiv.org/abs/math/0511744 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120614 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53Cxx | |
| dc.title | Generalized Doubling Constructions for Constant Mean Curvature Hypersurfaces in the (n+1)-Sphere | |
| dc.type | text |