25 citations · 36 across the 13 of their papers we have counts for
19 papers
Random hyperbolic polyhedra in horoballs
Florian Besau, Anna Gusakova, Christoph Thäle
We study the geodesic convex hull of a stationary Poisson point process restricted to a horoball in -dimensional hyperbolic space. The resulting random set is an unbounded hyper…
Sylvester's four point problem for ball-convex bodies
Alexandra Bakó-Szabó, Florian Besau, Ferenc Fodor
We investigate Sylvester's classical four-point problem for ball-convex bodies, where convex hulls are replaced by intersections of balls of a fixed radius . We show that the Ef…
Illumination Bodies in Projective Geometries
Rotem Assouline, Florian Besau, Elisabeth M. Werner
We extend the notion of illumination bodies to Riemannian spaces of constant curvature and to projective Finsler geometries. We prove that the derivative of their volume defines a…
Random convex chains through the lens of analytic combinatorics
Florian Besau, Christoph Thäle
Consider the triangle with vertices , , and . The lower boundary of the convex hull of , , together with independent uniformly distribute…
Random polytopes in convex bodies: Bridging the gap between extremal containers
Florian Besau, Anna Gusakova, Christoph Thäle
We investigate the asymptotic properties of random polytopes arising as convex hulls of independent random points sampled from a family of block-beta distributions. Notably, th…
The -floating area, curvature entropy, and isoperimetric inequalities on the sphere
Florian Besau, Elisabeth M. Werner
We explore analogs of classical centro-affine invariant isoperimetric inequalities, such as the Blaschke--Santaló inequality and the -affine isoperimetric inequalities, for co…
Floating bodies and duality in spaces of constant curvature
Florian Besau, Elisabeth M. Werner
We investigate a natural analog to Lutwak's -affine surface area in -dimensional spherical, hyperbolic and de Sitter space. In particular, we show that these curvature measur…
An intrinsic volume metric for the class of convex bodies in
Florian Besau, Steven Hoehner
A new intrinsic volume metric is introduced for the class of convex bodies in . As an application, an inequality is proved for the asymptotic best approximation of th…
Spherical convex hull of random points on a wedge
Florian Besau, Anna Gusakova, Matthias Reitzner +3
Consider two half-spaces and in whose bounding hyperplanes and are orthogonal and pass through the origin. The intersection $\mathbb{…
Random inscribed polytopes in projective geometries
Florian Besau, Daniel Rosen, Christoph Thäle
We establish central limit theorems for natural volumes of random inscribed polytopes in projective Riemannian or Finsler geometries. In addition, normal approximation of dual volu…
Asymptotic normality for random polytopes in non-Euclidean geometries
Florian Besau, Christoph Thäle
Asymptotic normality for the natural volume measure of random polytopes generated by random points distributed uniformly in a convex body in spherical or hyperbolic spaces is prove…
Asymptotic normality for random simplices and convex bodies in high dimensions
David Alonso-Gutiérrez, Florian Besau, Julian Grote +5
Central limit theorems for the log-volume of a class of random convex bodies in are obtained in the high-dimensional regime, that is, as . In particular,…
Intrinsic and Dual Volume Deviations of Convex Bodies and Polytopes
Florian Besau, Steven Hoehner, Gil Kur
We establish estimates for the asymptotic best approximation of the Euclidean unit ball by polytopes under a notion of distance induced by the intrinsic volumes. We also introduce…
Spherical centroid bodies
Florian Besau, Thomas Hack, Peter Pivovarov +1
The spherical centroid body of a centrally-symmetric convex body in the Euclidean unit sphere is introduced. Two alternative definitions - one geometric, the other probabilistic in…
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…
Weighted floating bodies and polytopal approximation
Florian Besau, Monika Ludwig, Elisabeth M. Werner
Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in hyperbolic space and to estab…
The floating body in real space forms
Florian Besau, Elisabeth M. Werner
We carry out a systematic investigation on floating bodies in real space forms. A new unifying approach not only allows us to treat the important classical case of Euclidean space…
The Spherical Convex Floating Body
Florian Besau, Elisabeth Werner
For a convex body on the Euclidean unit sphere the spherical convex floating body is introduced. The asymptotic behavior of the volume difference of a spherical convex body and its…
Binary Operations in Spherical Convex Geometry
Florian Besau, Franz E. Schuster
Characterizations of binary operations between convex bodies on the Euclidean unit sphere are established. The main result shows that the convex hull is essentially the only non-tr…