4 papers · 1 filter
Stability for barriers of n-dimensional convex bodies with surface area close to Jones' bound
Markus Kiderlen
Let be a convex body (a non-empty compact convex set) in -dimensional Euclidean space. A set is called a barrier (or an `opaque set') for if every line that intersec…
On the (outer) Minkowski content with lower-dimensional structuring element
Markus Kiderlen, Jan Rataj
Given a convex body (structuring element) and a set in a Euclidean space, we consider the -Minkowski content of . It is defined as the usual isotropic Minkowski conte…
Explicit lower bounds for opaque sets of unit square and unit disc
Markus Kiderlen, Florian Pausinger
Explicit lower bounds for the length of the shortest opaque set for the unit disc and the unit square in the Euclidean plane are derived. The results are based on an explicit appli…
A Blaschke-Petkantschin formula for linear and affine subspaces with application to intersection probabilities
Emil Dare, Markus Kiderlen, Christoph Thaele
Consider a uniformly distributed random linear subspace and a stochastically independent random affine subspace in , both of fixed dimension. For a natural cl…