Publication
Gluing constructions amongst constant mean curvature hypersurfaces in the (n+1)-sphere
AbstractFour constructions of constant mean curvature (CMC) hypersurfaces in the (n+1)-sphere are given, which should be considered analogues of ‘classical’ constructions that are possible for CMC hypersurfaces in Euclidean space. First, Delaunay-like hypersurfaces, consisting roughly of a chain of hyperspheres winding multiple times around an equator, are shown to exist for all the values of the mean curvature. Second, a hypersurface is constructed which consists of two chains of spheres winding around a pair of orthogonal equators, showing that Delaunay-like hypersurfaces can be fused together in a symmetric manner. Third, a Delaunay-like handle can be attached to a generalized Clifford torus of the same mean curvature. Finally, two generalized Clifford tori of equal but opposite mean curvature of any magnitude can be attached to each other by symmetrically positioned Delaunay-like ‘arms’. This last result extends Butscher and Pacard’s doubling construction for generalized Clifford tori of small mean curvature.
Download publicationRelated Resources
See what’s new.
2014
Design problem solving with biological analogies: A verbal protocol study
Biomimetic design applies biological analogies to solve design…
2013
Design Tools for the Rest of Us: Maker Hardware Requires Maker Software
In our own work, we are developing and applying a system which…
2017
Simulating Use Scenarios in Hospitals using Multi-Agent Narratives
Anticipating building-related complexities ensuing from occupants’…
2011
Planning to Fold Multiple Objects from a Single Self-Folding Sheet
This paper considers planning and control algorithms that enable a…
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