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- Martin Henk, John C. Wood
- 2006

spherical and hyperbolic space. It is divided into two equal-sized parts: the first is devoted to the two-dimensional case, where much more is known than in the n-dimensional setting, which is… (More)

- Bernd Gärtner, Martin Henk, Günter M. Ziegler
- Combinatorica
- 1998

- Martin Grötschel, Martin Henk
- Discrete & Computational Geometry
- 2003

A beautiful result of Bröcker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every d-dimensional polyhedron admits a representation as… (More)

- Martin Henk
- 2008

We show that for every lattice packing of n-dimensional spheres there exists an (n/ log2(n))-dimensional affine plane which does not meet any of the spheres in their interior, provided n is large… (More)

- Martin Henk, Jürgen Richter-Gebert, Günter M. Ziegler
- Handbook of Discrete and Computational Geometry…
- 2004

Convex polytopes are fundamental geometric objects that have been investigated since antiquity. The beauty of their theory is nowadays complemented by their importance for many other mathematical… (More)

- Ulrich Betke, Martin Henk
- Comput. Geom.
- 2000

Based on Minkowski’s work on critical lattices of 3-dimensional convex bodies we present an efficient algorithm for computing the density of a densest lattice packing of an arbitrary 3-polytope. As… (More)

- Martin Henk
- 2012

Before giving the mathematical description of the Löwner–John ellipsoids and pointing out some of their far-ranging applications, I briefly illuminate the adventurous life of the two eminent… (More)

- Martin Henk
- Inf. Process. Lett.
- 1997

K is a centrally symmetric convex body with nonempty interior and fK(·) is also called the distance function of K because fK(x) = min{ρ ∈ R≥0 : x ∈ ρK}. The Euclidean norm is denoted by fB(·), where… (More)

- Ulrich Betke, Martin Henk, Jörg M. Wills
- Discrete & Computational Geometry
- 1993

We show analogues of Minkowski’s theorem on successive minima, where the volume is replaced by the lattice point enumerator. We further give analogous results to some recent theorems by Kannan and… (More)

- Martin Henk
- 2002

The main purpose of this note is to prove an upper bound on the number of lattice points of a centrally symmetric convex body in terms of the successive minima of the body. This bound improves on… (More)