An area theorem for harmonic mappings with nonzero pole having quasiconformal extensions
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- by Bappaditya Bhowmik and Goutam Satpati;
- Proc. Amer. Math. Soc. 152 (2024), 3881-3891
- DOI: https://doi.org/10.1090/proc/16850
- Published electronically: July 26, 2024
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Abstract:
Let $\Sigma _H^k(p)$ be the class of sense-preserving univalent harmonic mappings defined on the open unit disk $\mathbb {D}$ of the complex plane with a simple pole at $z=p \in (0,1)$ that have $k$-quasiconformal extensions ($0\leq k<1$) onto the extended complex plane. In this article, we obtain an area theorem for this class of functions.References
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Bibliographic Information
- Bappaditya Bhowmik
- Affiliation: Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
- MR Author ID: 828284
- ORCID: 0000-0001-9171-3548
- Email: bappaditya@maths.iitkgp.ac.in
- Goutam Satpati
- Affiliation: Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
- MR Author ID: 1153551
- ORCID: 0000-0001-9125-3342
- Email: goutam.satpati@gmail.com
- Received by editor(s): September 21, 2023
- Received by editor(s) in revised form: September 27, 2023, March 4, 2024, and March 5, 2024
- Published electronically: July 26, 2024
- Additional Notes: The first author of this article was financially supported by SERB, India through Core Research Grant (Ref. No.- CRG/2022/001835). The second author of this article was financially supported by NBHM, DAE, Govt. of India (Ref. No. - 0204/3/2021/R&D-II/7248).
The first author is the corresponding author - Communicated by: Nageswari Shanmugalingam
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 3881-3891
- MSC (2020): Primary 31A05, 30C62, 30C55
- DOI: https://doi.org/10.1090/proc/16850
- MathSciNet review: 4781981