Extension of Holomorphic Functions: (34 De Gruyter Expositions in Mathematics)

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Aix-Marseille Université, France Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Table of Contents:
Riemann domains - Riemann domains over Cn; holomorphic functions; examples of Riemann regions; holomorphic extension of Riemann domains; the boundary of a Riemann domain; union, intersection, and direct limit of Riemann domains; domains of existence; maximal holomorphic extensions; liftings of holomorphic mappings I; holomorphic convexity; Riemann surfaces; pseudocenvexity - Plurisubharmonic functions; pseudoconvexity; the Kiselman minimum principle; d-operator; solution of the Levi problem; regular solutions; approximation; the Remmert embedding theorem; the Docquier-Grauert criteria; the division theorem; spectrum; liftings of holomorphic mappings II; envelopes of holomorphy for special domains - Univalent envelopes of holomorphy; k-tubular domains; matrix Reinhardt domains; the envelope of holomorphy of X/M; separately holomorphic functions; extension of meromorphic functions; existence domains of special families of holomorphic functions - special domains; the Ohsawa-Takegoshi extension theorem; the Skoda division theorem; the Catlin-Hakim-Sibony theorem; structure of envelopes of holomorphy.