## Hartogs Type Holomorphic Extensions

Prof. Roman Dwilewicz (Missouri University of Science and Technology, USA)

Abstract

in the talk there will be given a short review of holomorphic extension problems starting with the famous Hartogs theorem (1906), via Severi-Kneser-Fichera-Martinelli theorems, up to some recent results on global holomorphic extensions for unbounded domains obtained together with Al Boggess (Arizona State Univ.) and Zbigniew Slodkowski (Univ. Illinois at Chicago). The classical Hartogs theorem solves the extension problem for bounded domains in C^n and clearly shows the difference between one and many-variables cases. The theorem is considered as an informal beginning of Complex Analysis in Several Variables. Surprisingly, not many results are in the unbounded case even though it is important not only in Complex Analysis, but also in Partial Differential Equations and Algebraic Geometry. The problem appeared non-trivial and the work is in progress. The talk will be illustrated by many figures and pictures.