Titlebook: Introduction to Complex Analysis in Several Variables; Volker Scheidemann Textbook 2023Latest edition The Editor(s) (if applicable) and Th

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of elliptic boundary problems, compared to that on closed manifolds, still lagging behind in popularity? Admittedly, from an analytical point of view, it is a jigsaw puzzle which has more pieces than does the elliptic theory on closed manifolds. But that is not the only reason.978-1-4612-6713-3978-1-4612-0337-7

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Local Properties of Holomorphic Functions,Every student remembers from her or his first (or, at least, second) course on calculus that the function.

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Hints to the Exercises,In this chapter we give some hints to the exercises. This should help students to find solutions on their own. We give more hints to the exercises of the early chapters than to the exercises of the later chapters, because we believe that with growing experience on the subject the exercises should become a little more challenging.

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Continuation on Circular and Polycircular Domains,sion theorems (Riemann’s Removable Singularity Theorems, Hartogs’ Kugelsatz, Bochner’s Extension Theorem for tube domains) in the next chapters, finally leading to the notion of holomorphy domains and the theory of Cartan and Thullen.

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Analytic Sets, systems of equations. We will introduce the notion of codimension of an analytic set and show that in most cases analytic sets are “thin enough” that holomorphic functions defined outside an analytic set can be extended across the analytic set.