Published March 2022
| Submitted
Journal Article
Open
Bers slices in families of univalent maps
Abstract
We construct embeddings of Bers slices of ideal polygon reflection groups into the classical family of univalent functions Σ. This embedding is such that the conformal mating of the reflection group with the anti-holomorphic polynomial z ↦ ^(-d)z is the Schwarz reflection map arising from the corresponding map in Σ. We characterize the image of this embedding in Σ as a family of univalent rational maps. Moreover, we show that the limit set of every Kleinian reflection group in the closure of the Bers slice is naturally homeomorphic to the Julia set of an anti-holomorphic polynomial.
Additional Information
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021. Received 09 December 2020; Accepted 21 August 2021; Published 24 October 2021. The third author was supported by an endowment from Infosys Foundation and SERB research grant SRG/2020/000018.Attached Files
Submitted - 2007.02429.pdf
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2007.02429.pdf
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Additional details
- Eprint ID
- 112237
- DOI
- 10.1007/s00209-021-02871-y
- Resolver ID
- CaltechAUTHORS:20211206-221748427
- Infosys Foundation
- Science and Engineering Research Board (SERB)
- SRG/2020/000018
- Created
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2021-12-07Created from EPrint's datestamp field
- Updated
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2022-03-11Created from EPrint's last_modified field