38 citations · 56 across the 9 of their papers we have counts for
12 papers
Approximation of the Euclidean ball by polytopes with a fixed number of -faces
Steven Hoehner, Carsten Schütt, Elisabeth Werner
We derive lower estimates for the approximation of the -dimensional Euclidean ball by polytopes with a fixed number of -dimensional faces, . The metri…
Random approximation of convex bodies in Hausdorff metric
Joscha Prochno, Carsten Schütt, Mathias Sonnleitner +1
While there is extensive literature on approximation, deterministic as well as random, of general convex bodies in the symmetric difference metric, or other metrics arising fro…
Best and random approximation of a convex body by a polytope
Joscha Prochno, Carsten Schütt, Elisabeth M. Werner
In this paper, we give an overview of some results concerning best and random approximation of convex bodies by polytopes. We explain how both are linked and see that random approx…
The convex hull of random points on the boundary of a simple polytope
M. Reitzner, C. Schuett, E. M. Werner
The convex hull of N independent random points chosen on the boundary of a simple polytope in R^n is investigated. Asymptotic formulas for the expected number of vertices and facet…
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…
Floating functions
Ben Li, Carsten Schuett, Elisabeth M. Werner
We introduce floating bodies for convex, not necessarily bounded subsets of . This allows us to define floating functions for convex and log concave functions and log…
On the geometry of projective tensor products
Ohad Giladi, Joscha Prochno, Carsten Schütt +2
In this work, we study the volume ratio of the projective tensor products with . We obtain asymptotic…
The Surface Area Deviation of the Euclidean Ball and a Polytope
Steven D. Hoehner, Carsten Schuett, Elisabeth M. Werner
While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Her…
Dual Affine invariant points
Mathieu Meyer, Carsten Schuett, Elisabeth M. Werner
An affine invariant point on the class of convex bodies in R^n, endowed with the Hausdorff metric, is a continuous map p which is invariant under one-to-one affine transformations…
Combinatorial Inequalities and Subspaces of L1
Joscha Prochno, Carsten Schuett
Let M and N be Orlicz functions. We establish some combinatorial inequalities and show that the product spaces l^n_M(l^n_N) are uniformly isomorphic to subspaces of L_1 if M and N…
A convex body whose centroid and Santaló point are far apart
Mathieu Meyer, Carsten Schütt, Elisabeth M. Werner
We give an example of a convex body whose centroid and Santaló point are "far apart".
Umbrellas and polytopal approximation of the euclidean ball
Yehoram Gordon, Shlomo Reisner, Carsten Schütt
There are two positive, absolute constants and so that the volume of the difference set of the -dimensional Euclidean ball and an inscribed polytope with n verti…