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

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

2005-11-30

arxiv.org/abs/math/0511744v2

Mathematics

Differential Geometry

18 pages. Final revised version accepted for publication in Annals of Global Analysis and Geometry

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Generalized Doubling Constructions for Constant Mean Curvature Hypersurfaces in the (n+1)-Sphere does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Doubling Constructions for Constant Mean Curvature Hypersurfaces in the (n+1)-Sphere, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Doubling Constructions for Constant Mean Curvature Hypersurfaces in the (n+1)-Sphere will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-430135