Singularities of convex hulls of smooth hypersurfaces

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We describe singularities of the convex hull of a generic compact smooth hypersurface in four-dimensional affine space up to diffeomorphisms. It turns out there are only two new singularities (in comparison with the previous dimension case) which appear at separate points of the boundary of the convex hull and are not removed by a small perturbation of the original hypersurface. The first singularity does not contain functional, but has at least nine continuous number invariants. A normal form which does not contain invariants at all is found for the second singularity.
combined version of the two journal papers indicated below

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Metric Geometry, 58K40; 52A20

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http://salesiana.dossiersoluciones.com/handle/123456789/66528

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0302173
 http://arxiv.org/abs/math/0302173
 Proc. Steklov Inst. Math., 221 (1998), 71--90; Banach Center Publ., 50 (1999), 61--74

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arXiv