Tout chemin générique de hérissons réalisant un retournement de la sphère dans R3 comprend un hérisson porteur de queues d'aronde positives
Martinez-Maure, Yves (Institut Mathématique de Jussieu (París, França))
Date: |
2015 |
Abstract: |
Hedgehogs are (possibly singular and self-intersecting) hypersurfaces that describe Minkowski differences of convex bodies in Rn+1. They are the natural geometrical objects when one seeks to extend parts of the Brunn-Minkowski theory to a vector space which contains convex bodies. In this paper, we prove that in every generic path of hedgehogs performing the eversion of the sphere in R3, there exists a hedgehog that has positive swallowtails. This study was motivated by an open problem raised in 1985 by Langevin, Levitt, and Rosenberg. |
Rights: |
Tots els drets reservats. |
Language: |
Francès |
Document: |
Article ; recerca ; Versió publicada |
Subject: |
Eversion of the sphere ;
Hedgehogs ;
Generic metamorphosis ;
Type of swallowtails ;
Indices ;
Absolute coorientation |
Published in: |
Publicacions matemàtiques, Vol. 59 Núm. 2 (2015) , p. 339-351 (Articles) , ISSN 2014-4350 |
Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/295189
DOI: 10.5565/PUBLMAT_59215_04
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Record created 2015-07-03, last modified 2022-09-04