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Weighted cone-volume measures of pseudo-cones
Rolf Schneider
A pseudo-cone in is a nonempty closed convex set not containing the origin and such that for all . It is called a -pseudo-cone if $C…
Vectorial analogues of Cauchy's surface area formula
Daniel Hug, Rolf Schneider
Cauchy's surface area formula says that for a convex body in -dimensional Euclidean space the mean value of the -dimensional volumes of the orthogonal projections of…
The typical irregularity of virtual convex bodies
Rolf Schneider
The semigroup of convex bodies in with Minkowski addition has a canonical embedding into an abelian group; its elements have been called virtual convex bodies. Geom…
Typical curvature behaviour of bodies of constant width
Imre Barany, rolf Schneider
It is known that an -dimensional convex body which is typical in the sense of Baire category, shows a simple, but highly non-intuitive curvature behaviour: at almost all of its…