CaltechAUTHORS
  A Caltech Library Service

Bers slices in families of univalent maps

Lazebnik, Kirill and Makarov, Nikolai G. and Mukherjee, Sabyasachi (2022) Bers slices in families of univalent maps. Mathematische Zeitschrift, 300 (3). pp. 2771-2808. ISSN 0025-5874. doi:10.1007/s00209-021-02871-y. https://resolver.caltech.edu/CaltechAUTHORS:20211206-221748427

[img] PDF - Submitted Version
See Usage Policy.

3MB

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20211206-221748427

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00209-021-02871-yDOIArticle
https://rdcu.be/cCI4YPublisherFree ReadCube access
https://arxiv.org/abs/2007.02429arXivDiscussion Paper
ORCID:
AuthorORCID
Lazebnik, Kirill0000-0001-8963-4410
Mukherjee, Sabyasachi0000-0002-6868-6761
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.
Funders:
Funding AgencyGrant Number
Infosys FoundationUNSPECIFIED
Science and Engineering Research Board (SERB)SRG/2020/000018
Subject Keywords:Schwarz Reflection Mappings; Sullivan’s dictionary; Reflection groups; Univalent Mappings; Combination theorems; Quadrature Domains
Issue or Number:3
Classification Code:Mathematics Subject Classification: 30C10; 37F10
DOI:10.1007/s00209-021-02871-y
Record Number:CaltechAUTHORS:20211206-221748427
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20211206-221748427
Official Citation:Lazebnik, K., Makarov, N.G. & Mukherjee, S. Bers slices in families of univalent maps. Math. Z. 300, 2771–2808 (2022). https://doi.org/10.1007/s00209-021-02871-y
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112237
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Dec 2021 17:29
Last Modified:11 Mar 2022 23:23

Repository Staff Only: item control page