Titlebook: Geometric Function Theory in Higher Dimension; Filippo Bracci Book 2017 Springer International Publishing AG, part of Springer Nature 2017

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https://doi.org/10.1007/978-94-009-7261-2In this paper we show the equivalence among three conjectures (and related open questions), namely, the embedding of univalent maps of the unit ball into Loewner chains, the approximation of univalent maps with entire univalent maps and the immersion of domain biholomorphic to the ball in a Runge way into Fatou-Bieberbach domains.

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Decades of Improvement: The Interwar Years,We give an example of a domain . in ., biholomorphic to a ball, such that . is not Runge in any Stein neighborhood of ..

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The Embedding Conjecture and the Approximation Conjecture in Higher Dimension,In this paper we show the equivalence among three conjectures (and related open questions), namely, the embedding of univalent maps of the unit ball into Loewner chains, the approximation of univalent maps with entire univalent maps and the immersion of domain biholomorphic to the ball in a Runge way into Fatou-Bieberbach domains.

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Jordan Structures in Bounded Symmetric Domains,We discuss how Jordan algebraic structures arise from the geometry of bounded symmetric domains and their useful role in the study of holomorphic functions on these domains.

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On Runge Neighborhoods of Closures of Domains Biholomorphic to a Ball,We give an example of a domain . in ., biholomorphic to a ball, such that . is not Runge in any Stein neighborhood of ..

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,Metric Properties of Domains in ℂ,,This article is the written form of a presentation given during the Workshop “Geometric Function Theory in higher dimension”. We present some developments in the classical field of classification of domains in . and some related questions.

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978-3-030-10319-4Springer International Publishing AG, part of Springer Nature 2017