Worldwide Sites

You have been detected as being from . Where applicable, you can see country-specific product information, offers, and pricing.

Change country/language X

Keyboard ALT + g to toggle grid overlay

Generalized doubling constructions for constant mean curvature hypersurfaces in the (n+1)-sphere

Adrian Butscher, F. Pacard

Annals of Global Analysis and Geometry
2007

Abstract

The (n+1)-sphere contains a simple family of constant mean curvature (CMC) hypersurfaces equal to products of a p-sphere and a 1-sphere of different radii, called the generalized Clifford hypersurfaces. This paper demonstrates that two 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 previous results of the authors.

Related Publications

Related Projects

Heading

Descriptive text. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt magna aliqua in reprehenderit.

Heading

Descriptive text. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt magna aliqua in reprehenderit.

Heading

Descriptive text. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt magna aliqua in reprehenderit.