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Proceedings of the American Mathematical Society

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A note on convex conformal mappings


Authors: Martin Chuaqui and Brad Osgood
Journal: Proc. Amer. Math. Soc. 147 (2019), 2655-2659
MSC (2010): Primary 30C45; Secondary 30C80, 30C62
DOI: https://doi.org/10.1090/proc/14429
Published electronically: March 5, 2019
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Abstract | References | Similar Articles | Additional Information

Abstract: We establish a new characterization for a conformal mapping of the unit disk $ \mathbb{D}$ to be convex, and identify the mappings onto a half-plane or a parallel strip as extremals. We also show that, with these exceptions, the level sets of $ \lambda $ of the Poincaré metric $ \lambda \vert dw\vert$ of a convex domain are strictly convex.


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Additional Information

Martin Chuaqui
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenue Vicuana Mackenna 4860, Santiago, Chile
Email: mchuaqui@mat.uc.cl

Brad Osgood
Affiliation: Department of Electrical Engineering, Stanford University, 271 Packard Building, Stanford, California 94305
Email: osgood@stanford.edu

DOI: https://doi.org/10.1090/proc/14429
Keywords: Convex mapping, Poincar\'e metric, level set, curvature
Received by editor(s): August 7, 2018
Received by editor(s) in revised form: October 8, 2018
Published electronically: March 5, 2019
Additional Notes: The first author was partially supported by Fondecyt Grant #1150115.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2019 American Mathematical Society