153 citations · 485 across the 45 of their papers we have counts for
5 papers · 1 filter
A Steiner formula in the Brunn Minkowski theory
Kateryna Tatarko, Elisabeth M. Werner
We prove an analogue of the classical Steiner formula for the affine surface area of a Minkowski outer parallel body for any real parameters . We show that the classical S…
Surface area deviation between smooth convex bodies and polytopes
Julian Grote, Christoph Thaele, Elisabeth M. Werner
The deviation of a general convex body with twice differentiable boundary and an arbitrarily positioned polytope with a given number of vertices is studied. The paper considers the…
Data depth and floating body
Stanislav Nagy, Carsten Schuett, Elisabeth M. Werner
Little known relations of the renown concept of the halfspace depth for multivariate data with notions from convex and affine geometry are discussed. Halfspace depth may be regarde…
Flag numbers and floating bodies
Florian Besau, Carsten Schütt, Elisabeth M. Werner
We investigate weighted floating bodies of polytopes. We show that the weighted volume depends on the complete flags of the polytope. This connection is obtained by introducing fla…
Ulam Floating Body
Han Huang, Boaz A. Slomka, Elisabeth M. Werner
We study a new construction of bodies from a given convex body in which are isomorphic to (weighted) floating bodies. We establish several properties of this new c…