Abstract
Hedgehogs are (possibly singular and self-intersecting) hypersurfaces that describe Minkowski differences of convex bodies in $\mathbb{R}^{n+1}$. 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 $\mathbb{R}^{3}$, there exists a hedgehog that has positive swallowtails. This study was motivated by an open problem raised in 1985 by Langevin, Levitt, and Rosenberg.
Citation
Yves Martinez-Maure. "Tout chemin générique de hérissons réalisant un retournement de la sphère dans $\mathbb{R}^{3}$ comprend un hérisson porteur de queues d'aronde positives." Publ. Mat. 59 (2) 339 - 351, 2015.
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