Tout chemin générique de hérissons réalisant un retournement de la sphère dans R3 comprend un hérisson porteur de queues d’aronde positives

• Autores: Yves Martínez-Maure
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 59, Nº 2, 2015, págs. 339-351
• Idioma: francés
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• Resumen

  • 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.