328 research outputs found
The Orlicz version of the Minkowski problem on for
An Orlicz version of the -Minkowski problem on is discussed
corresponding to the case
Intrinsic volumes of random polytopes with vertices on the boundary of a convex body
Let be a convex body in , let , and let
be a positive and continuous probability density function with
respect to the -dimensional Hausdorff measure on the boundary of . Denote by the convex hull of points chosen randomly and
independently from according to the probability distribution
determined by . For the case when is a submanifold
of with everywhere positive Gauss curvature, M. Reitzner proved an
asymptotic formula for the expectation of the difference of the th intrinsic
volumes of and , as . In this article, we extend this
result to the case when the only condition on is that a ball rolls freely
in
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