The Embedding Conjecture and the Approximation Conjecture in Higher Dimension

  • Matteo FiacchiEmail author
Part of the Springer INdAM Series book series (SINDAMS, volume 26)


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.


Loewner theory Embedding problems Approximation of univalent maps 

Mathematics Subject Classification

32E30 32A10 



The author would like to express his gratitude to Prof. Filippo Bracci for his availability and for introducing him into Loewner theory.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Dipartimento Di MatematicaUniversità di Roma “Tor Vergata”RomaItaly

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