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Cousin-I spaces and domains of holomorphy

Ilie BârzăViorel Vâjâitu — 2009

Annales Polonici Mathematici

We prove that a Cousin-I open set D of an irreducible projective surface X is locally Stein at every boundary point which lies in X r e g . In particular, Cousin-I proper open sets of ℙ² are Stein. We also study K-envelopes of holomorphy of K-complete spaces.

Blaschke product generated covering surfaces

Ilie BarzaDorin Ghisa — 2009

Mathematica Bohemica

It is known that, under very general conditions, Blaschke products generate branched covering surfaces of the Riemann sphere. We are presenting here a method of finding fundamental domains of such coverings and we are studying the corresponding groups of covering transformations.

Dynamics of dianalytic transformations of Klein surfaces

Ilie BarzaDorin Ghisa — 2004

Mathematica Bohemica

This paper is an introduction to dynamics of dianalytic self-maps of nonorientable Klein surfaces. The main theorem asserts that dianalytic dynamics on Klein surfaces can be canonically reduced to dynamics of some classes of analytic self-maps on their orientable double covers. A complete list of those maps is given in the case where the respective Klein surfaces are the real projective plane, the pointed real projective plane and the Klein bottle.

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