Singularities of convex hulls of smooth hypersurfaces

摘要

We describe singularities of the convex hull of a generic compact smoothhypersurface in four-dimensional affine space up to diffeomorphisms. It turnsout there are only two new singularities (in comparison with the previousdimension case) which appear at separate points of the boundary of the convexhull and are not removed by a small perturbation of the original hypersurface.The first singularity does not contain functional, but has at least ninecontinuous number invariants. A normal form which does not contain invariantsat all is found for the second singularity.