Generalized Doubling Constructions for Constant Mean Curvature Hypersurfaces in the (n+1)-Sphere

dc.creatorButscher, Adrian
dc.creatorPacard, Frank
dc.date2005-11-30
dc.date2006-12-23
dc.date.accessioned2026-07-07T07:36:58Z
dc.date.available2026-07-07T07:36:58Z
dc.descriptionThe (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.description18 pages. Final revised version accepted for publication in Annals of Global Analysis and Geometry
dc.identifierhttps://arxiv.org/abs/math/0511744
dc.identifierhttp://arxiv.org/abs/math/0511744
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120614
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject53Cxx
dc.titleGeneralized Doubling Constructions for Constant Mean Curvature Hypersurfaces in the (n+1)-Sphere
dc.typetext

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