24 feb 2015 -- 16:00
Aula D'Antoni, Dip. Matematica, Università "Tor Vergata", Roma
By work of E. Poletsky the polynomial hull of a compact K in Cn can be described by analytic discs with boundaries contained in an arbitrary neighborhood of K except for the image of a set of arbitrarily small length. Easy examples of disconnected compacts show that one cannot always arrange that the whole boundary is close to K. On the other hand, this is known to be possible for certain connected compacts. In particular, this is shown by B. Drinovec Drnovšek and F. Forstnerič for connected compacts which are invariant under the standard circle action. Moreover they raise the question whether this remains valid for connected compacts in general. We will explain a counter-example, showing that the answer is negative.