13 citations · 62 across the 26 of their papers we have counts for
26 papers · 1 filter
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…
Pseudo-cones
Rolf Schneider
Pseudo-cones are a class of unbounded closed convex sets, not containing the origin. They admit a kind of polarity, called copolarity. With this, they can be considered as a counte…
Minkowski type theorems for convex sets in cones
Rolf Schneider
Minkowski's classical existence theorem provides necessary and sufficient conditions for a Borel measure on the unit sphere of Euclidean space to be the surface area measure of a c…
Random Gale diagrams and neighborly polytopes in high dimensions
Rolf Schneider
Taking up a suggestion of David Gale from 1956, we generate sets of combinatorially isomorphic polytopes by choosing their Gale diagrams at random. We find that in high dimensions,…
Integral geometry of pairs of hyperplanes or lines
Daniel Hug, Rolf Schneider
Crofton's formula of integral geometry evaluates the total motion invariant measure of the set of -dimensional planes having nonempty intersection with a given convex body. This…
Separation bodies: a conceptual dual to floating bodies
Rolf Schneider
Let be a convex body in Euclidean space , and let a translation invariant, locally finite Borel measure on the space of hyperplanes in be given.…