Workshop

On convex (concave) roofs

  • Armin Uhlmann (Universität Leipzig)
A3 01 (Sophus-Lie room)

Abstract

Given a function g on the exrtremal points of a convex compact set K, one may ask for the largest convex extension g of g on K. Similar the smallest concave extension g ist defined. Entanglement of formation, entanglement of assistance, some concurrences belong to these classes of functions. If the extreme boundary of K is also compact and g is continuous, then a remarkable phenomenon takes place: K is covered by convex subsets on each of which the extension, say g, is affine, and every one of these subsets is convexly generated by some extremal points of K . Because of this I have called g and g "roofs" . I try to explain how to use this as a tool and I show the structure of some of the known examples, with and without bifurcations.

Antje Vandenberg

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Nihat Ay

Max Planck Institute for Mathematics in the Sciences