On the smoothness of the equizonal ovaloids
type: Item
instance of: scholarly article
title: On the smoothness of the equizonal ovaloids
zbMATH Open document ID: 1283.53004
author: Jeff Dodd
author: Michael Harrison
author: Vincent Coll
published in: Journal of Geometry
publication date: 2013-04-08T00:00:00Z
review text: The generalized equal area zones property demands that the \(n\)-volume of a ``hyperzone'' sliced out of the hypersurface of revolution by two parallel hyperplanes orthogonal to the axis of rotation be proportional to the distance between the hyperplanes. For each \(n \geq 2\), there is, up to scaling, a unique closed strictly convex \(n\)-dimensional hypersurface of revolution in \(\mathbb R^{n+1},\) of class \(C^1\), satisfying the generalized equal area zones property. When \(n=2\), this object is the ordinary sphere, but for \(n>2\) it is a more exotic object, the equizonal \(n\)-ovaloid \(\mathrm{EO}^n\). Dodd and Coll in 2008 reported that if \(n\) is even, then \(\mathrm{EO}^n\) is of class \(C^\infty\), and if \(n\) is odd, \(\mathrm{EO}^n\) is of class \(C^{(n-1)/2}\). The authors show that if \(n\) is even, \(\mathrm{EO}^n\) is analytic, and that if \(n\) is odd, \(\mathrm{EO}^n\) is analytic everywhere except at its two poles where it is of class exactly \(C^{n-1}\).
reviewed by: Maria Aparecida Soares Ruas
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 26A46
zbMATH DE Number: 6151651
zbMATH Keywords: equizonal ovaloids
zbMATH Keywords: equal area zones property
zbMATH Keywords: hypersurfaces of revolution
zbMATH Keywords: analytic
zbMATH Keywords: smoothness
MaRDI profile type: Publication
full work available at URL: s00022-012-0135-1
OpenAlex ID: W2017667894
cites work: Generalizing the equal area zones property of the sphere
cites work: The Equal Area Zones Property
cites work: Umkehrung eines Satzes von Archimedes über die Kugel
cites work: Q5846853
DOI: 10.1007/S00022-012-0135-1
description: scientific article; zbMATH DE number 6151651