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Nitsche type inequality for hyperbolic harmonic mappings between annuli in the unit ball \(\mathbb {B}^3\)

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Abstract

We prove a Nitsche type inequality for hyperbolic harmonic mappings between rings in the hyperbolic ball \(\mathbb {B}^3\subset \mathbb {R}^3\). It states the following: there is a positive function \(\Phi (a,b)\), so if there exists a hyperbolic harmonic mapping of a spherical annulus \(\mathbb {A}(a,b)\subset \mathbb {B}^3\) onto a spherical annulus \(\mathbb {A}(1,R)\), then \(R\ge 1+\Phi (a,b)\). The best such function \(\Phi \) is explicitly estimated and conjectured.

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  1. University of Montenegro, Faculty of Natural Sciences and Mathematics, Cetinjski put b.b, 81000, Podgorica, Montenegro

    David Kalaj

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  1. David Kalaj
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Kalaj, D. Nitsche type inequality for hyperbolic harmonic mappings between annuli in the unit ball \(\mathbb {B}^3\). Anal.Math.Phys. 13, 57 (2023). https://doi.org/10.1007/s13324-023-00820-y

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  • DOI: https://doi.org/10.1007/s13324-023-00820-y

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