|Location:||MSRI: Baker Board Room|
Let K be a compact convex set in R^d which is an intersection of halfspaces defined by at most two coordinates. Let Q be the smallest axes-parallel box containing K.
We show that when the dimension d grows, the ratio of the diameters (diam Q/diam K) of the two sets can be arbitrarily large. How large exactly is open.
In Hilbert space every closed convex subset is contractive, that is, it is the fixed point set of a 1-Lipschitz mapping. In l_p-spaces, p not equal to 2, the contractive sets are known to be precisely the closed convex sets which are an intersection of halfspaces defined by at most two coordinates.No Notes/Supplements Uploaded No Video Files Uploaded