POLYNOMIAL HULLS AND ENVELOPES OF HOLOMORPHY OF SUBSETS OF STRICTLY PSEUDOCONVEX BOUNDARIES

First we give a construction of a Cantor set in the unit sphere in ℂ3 the polynomial hull of which contains interior points. Such sets were known to exist in spheres in ℂ2. Secondly, we construct an open connected subset of the unit sphere in ℂ3 with infinitely sheeted envelope of holomorphy.

ENVELOPE OF HOLOMORPHY OF CERTAIN TWO-MANIFOLDS IN ℂ2

We study two-spheres Γ with isolated complex tangencies of high order of tangency. We show that under certain conditions the envelope of holomorphy of such two-sphere is a three-surface M foliated by complex discs and the boundary of M is Γ.