Diameter and displacement of sphere involutions
Renato G. Bettiol, Emilio A. Lauret
TL;DR
This paper proves that in all dimensions three and above, spheres can be deformed to increase their diameter beyond the distance between antipodal points, resolving a question posed by Nikonorov.
Contribution
It demonstrates a deformation of spheres in all dimensions ≥3 to surpass antipodal point distances, answering an open question.
Findings
Spheres in all dimensions ≥3 can be deformed to increase diameter.
The diameter can be made larger than the antipodal distance.
It provides a positive answer to Nikonorov's question.
Abstract
We show that spheres in all dimensions can be deformed to have diameter larger than the distance between any pair of antipodal points. This answers a question of Yurii Nikonorov.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Mathematics and Applications · Point processes and geometric inequalities