3 citations · 14 across the 20 of their papers we have counts for
37 papers
Minkowski's successive minima in convex and discrete geometry
Iskander Aliev, Martin Henk
In this short survey we want to present some of the impact of Minkowski's successive minima within Convex and Discrete Geometry. Originally related to the volume of an -symmetri…
Polynomial Bounds in Koldobsky's Discrete Slicing Problem
Ansgar Freyer, Martin Henk
In 2013, Koldobsky posed the problem to find a constant , depending only on the dimension , such that for any origin-symmetric convex body there exis…
On subspace concentration for dual curvature measures
Katharina Eller, Martin Henk
We study subspace concentration of dual curvature measures of convex bodies satisfying for some . We present upper bounds on the subspace concent…
New Bounds for the Integer Carathéodory Rank
Iskander Aliev, Martin Henk, Mark Hogan +2
Given a rational pointed -dimensional cone , we study the integer Carathéodory rank and its asymptotic form , where we co…
Affine Subspace Concentration Conditions for Centered Polytopes
Ansgar Freyer, Martin Henk, Christian Kipp
Recently, K.-Y. Wu introduced affine subspace concentration conditions for the cone volumes of polytopes and proved that the cone volumes of centered, reflexive, smooth lattice pol…
On lattice width of lattice-free polyhedra and height of Hilbert bases
Martin Henk, Stefan Kuhlmann, Robert Weismantel
We study the lattice width of lattice-free polyhedra given by in terms of , the maximal minor in absolute value of $…