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Proceedings of the American Mathematical Society

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On Heinz-type inequality for the half-plane and Gaussian curvature of minimal surfaces


Author: David Kalaj
Journal: Proc. Amer. Math. Soc. 148 (2020), 1757-1764
MSC (2010): Primary 53A10
DOI: https://doi.org/10.1090/proc/14852
Published electronically: December 30, 2019
MathSciNet review: 4069212
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Abstract: We prove a Heinz-type inequality for harmonic diffeomorphisms of the half-plane onto itself. We then apply this result to prove certain sharp bound of the Gaussian curvature of a minimal surface, provided that it lies above the whole half-plane in $\mathbf {R}^3$.


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Additional Information

David Kalaj
Affiliation: Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put b.b. 81000 Podgorica, Montenegro
MR Author ID: 689421
Email: davidk@ucg.ac.me

Keywords: Subharmonic functions, harmonic mappings, minimal surfaces
Received by editor(s): January 2, 2019
Received by editor(s) in revised form: April 13, 2019, May 18, 2019, August 22, 2019, and August 28, 2019
Published electronically: December 30, 2019
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2019 American Mathematical Society