Hartogs extension phenomena for analytic curves.
Hartogs type extension theorems on some domains in Kähler manifolds
Given a locally pseudoconvex bounded domain Ω, in a complex manifold M, the Hartogs type extension theorem is said to hold on Ω if there exists an arbitrarily large compact subset K of Ω such that every holomorphic function on Ω-K is extendible to a holomorphic function on Ω. It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is compact Kähler and...
Holomorphe Korrespondenzen und meromorphe Abbildungen allgemeiner komplexer Räume.
Holomorphic and Meromorphic Mappings and Curvature.
Holomorphic and Meromorphic Mappings and Curvature. II.
Holomorphic equivalence and proper mapping of bounded Reinhardt domains not containing the origin.
Holomorphic extension from the sphere to the ball in Hilbert space
Holomorphic extension of generalizations of functions.
Holomorphic extension of generalizations of functions. II.
Holomorphic extension to open hulls
Holomorphic extensions of formal objects
We are interested on families of formal power series in parameterized by (). If every is a polynomial whose degree is bounded by a linear function ( for some and ) then the family is either convergent or the series for all except a pluri-polar set. Generalizations of these results are provided for formal objects associated to germs of diffeomorphism (formal power series, formal meromorphic functions, etc.). We are interested on describing the nature of the set of parameters where...
Holomorphic functions with singularities on algebraic sets.
How to prove Fefferman's theorem without use of differential geometry