Singularities of convex hulls of smooth hypersurfaces

Details Singularities of convex hulls of smooth hypersurfaces Singularities of convex hulls of smooth hypersurfaces

2003-02-14

arxiv.org/abs/math/0302173v1

Proc. Steklov Inst. Math., 221 (1998), 71--90; Banach Center Publ., 50 (1999), 61--74

Mathematics

Metric Geometry

combined version of the two journal papers indicated below

Scientific paper

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.

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