A family of flat Minkowski planes over convex functions

A family of flat Minkowski planes admitting 3-dimensional simple groups of automorphisms

In this paper we construct a new family of flat Minkowski planes of group dimension 3. These planes share the positive half with the classical real Minkowski plane and admit simple groups of automorphisms isomorphic to PSL2ðRÞ acting diagonally on the torus. We further determine the full automorphism groups and the Klein–Kroll types of these flat Minkowski planes. 2000 Mathematics Subject Class...

Cutting-Planes for Optimization of Convex Functions over Nonconvex Sets

We derive linear inequality characterizations for sets of the form conv{(x, q) ∈ R×R : q ≥ Q(x), x ∈ R − int(P )} where Q is convex and differentiable and P ⊂ R. We show that in several cases our characterization leads to polynomial-time separation algorithms that operate in the original space of variables, in particular when Q is a positive-definite quadratic and P is a polyhedron or an ellips...

On the Klein–Kroll types of flat Minkowski planes

Klein and Kroll classified Minkowski planes with respect to subgroups of central automorphisms and obtained a multitude of types. Some of these types are known to exist only in finite Minkowski planes or as the type of a proper subgroup in the automorphism group. In this paper we investigate the Klein– Kroll types of flat Minkowski planes with respect to the full automorphism groups of these pl...

Minkowski valuations on convex functions

A classification of [Formula: see text] contravariant Minkowski valuations on convex functions and a characterization of the projection body operator are established. The associated LYZ measure is characterized. In addition, a new [Formula: see text] covariant Minkowski valuation on convex functions is defined and characterized.

Minkowski Planes with Miquelian Pairs