13 citations · 62 across the 26 of their papers we have counts for
40 papers
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…
Random zonotopes and valuations
Rolf Schneider
We define a random zonotope in Euclidean space, by adding finitely many random segments, which are independently and identically distributed. For this random polytope, we determine…
Another look at threshold phenomena for random cones
Daniel Hug, Rolf Schneider
In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passe…
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,…