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.
2021
RobustPointSet: A Dataset for Benchmarking Robustness of Point Cloud ClassifiersThe 3D deep learning community has seen significant strides in…
2022
AvatAR: An Immersive Analysis Environment for Human Motion Data Combining Interactive 3D Avatars and TrajectoriesAnalysis of human motion data can reveal valuable insights about the…
2014
Active Printed Materials for Complex Self-Evolving DeformationsWe propose a new design of complex self-evolving structures that vary…
2010
Multi-Objective Optimization in ArchitectureThe challenge of the architect is to create a high performing building…
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