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.
2024
Optimization of Large-scale Aeroengine Parts Produced by Additive ManufacturingThis research demonstrates the transformative potential of Additive…
2024
Project Reframe: A Leap into VR Motion Capture and EditingExplore Project Reframe for recording and editing motion in Virtual…
2023
Explore Design and Make with Autodesk Research at AU 2023Get ready for AU 23 and learn more about how we’re working to solve…
2013
Skillometers: Reflective Widgets that Motivate and Help Users to Improve PerformanceApplications typically provide ways for expert users to increase their…
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