Abstract
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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Acknowledgements
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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Fiacchi, M. (2017). The Embedding Conjecture and the Approximation Conjecture in Higher Dimension. In: Bracci, F. (eds) Geometric Function Theory in Higher Dimension. Springer INdAM Series, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-73126-1_1
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DOI: https://doi.org/10.1007/978-3-319-73126-1_1
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Online ISBN: 978-3-319-73126-1
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