Publication

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

AbstractThe (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.

Download publication

Related Resources

See what’s new.

Publication

2006

Performing Incremental Bayesian Inference by Dynamic Model Counting

The ability to update the structure of a Bayesian network when new…

Publication

2021

Design guidelines for laser powder bed fusion in Inconel 718

Additive manufacturing (AM) has been leveraged across various…

Publication

2013

Comparison of User Performance in Mixed 2D-3D Multi-Display Environments

Stereoscopic displays and volumetric 3D displays capable of delivering…

Publication

2012

Efficient Geometrically Exact Continuous Collision Detection

Continuous collision detection (CCD) between deforming triangle mesh…

Get in touch

Something pique your interest? Get in touch if you’d like to learn more about Autodesk Research, our projects, people, and potential collaboration opportunities.

Contact us