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5 papers · 1 filter
Siciak-Zahariuta extremal functions, analytic discs and polynomial hulls
Finnur Larusson, Ragnar Sigurdsson
We prove two disc formulas for the Siciak-Zahariuta extremal function of an arbitrary open subset of complex affine space. We use these formulas to characterize the polynomial hull…
The Penrose Transform for Complex Projective Space
Michael Eastwood
Various complexes of differential operators are constructed on complex projective space via the Penrose transform, which also computes their cohomology.
Schlicht envelopes of holomorphy and foliations by lines
Finnur Larusson, Rasul Shafikov
Given a domain Y in a complex manifold X, it is a difficult problem with no general solution to determine whether Y has a schlicht envelope of holomorphy in X, and if it does, to d…
Siciak-Zahariuta extremal functions and polynomial hulls
Finnur Larusson, Ragnar Sigurdsson
We use our disc formula for the Siciak-Zahariuta extremal function to characterize the polynomial hull of a connected compact subset of complex affine space in terms of analytic di…
Examples of Unbounded Homogeneous Domains in Complex Space
Michael Eastwood, Alexander Isaev
We construct several new examples of homogeneous domains in complex space that do not have bounded realisations. They are equivalent to tubes over affinely homogeneous domains in r…