Hedgehogs and area of order 2
type: Item
instance of: scholarly article
title: Hedgehogs and area of order 2
zbMATH Open document ID: 0858.53004
DOI: 10.1007/BF01268931
author: Yves Martinez-Maure
published in: Archiv der Mathematik
publication date: 1997-03-10T00:00:00Z
review text: We define an algebraic area of order 2 for hedgehogs (envelopes parametrized by their Gauss map) in \(E^{n+1}\). On the vector space of hedgehogs defined up to a translation, this yields a nondegenerate quadratic form that allows us to define a scalar product on some subspaces, such as the subspace of projective hedgehogs. As an application, we give some characterizations of spheres among all convex hedgehogs of constant width. Finally, we prove that for minimal hedgehogs of finite area in \(E^3\) the square root of the area is a convex function of the support function, and we extend this result to asymptotic areas of embedded ends.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 52A38
zbMATH DE Number: 938588
zbMATH Keywords: envelopes parametrized by their Gauss map
zbMATH Keywords: convex hypersurfaces
zbMATH Keywords: minimal surfaces of finite area
zbMATH Keywords: constant width
MaRDI profile type: Publication
cites work: A maximum principle at infinity for minimal surfaces and applications
cites work: On projective hedgehogs (envelopes parametrized by their Gauss map)
cites work: Q4865390
cites work: Q5611582
cites work: Q5287551
cites work: Uniqueness, symmetry, and embeddedness of minimal surfaces
cites work: Q5774640
full work available at URL: https://doi.org/10.1007/bf01268931
OpenAlex ID: W2032676329
description: scientific article; zbMATH DE number 938588