# Polynomial hulls and boundary behavior of analytic discs

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Egmont Porten

created by risa on 19 Feb 2015

24 feb 2015
-- 16:00

Aula D'Antoni, Dip. Matematica, Università "Tor Vergata", Roma

**Abstract.**

By work of E. Poletsky the polynomial hull of a compact K in C^{n} 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.