Curvatures of typical convex bodies—the complete picture
نویسنده
چکیده
It is known that a typical n-dimensional convex body, in the Baire category sense, has the property that its set of umbilics of zero curvature has full measure in the boundary of the body. We show that a typical convex body has in addition the following properties. The spherical image of the set of umbilics of zero curvature has measure zero. The set of umbilics of infinite curvature is dense in the boundary and uncountable and its spherical image has full measure in the unit sphere.
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