Quasi-Nearly Subharmonic Functions and QC Mappings

Vesna Todorčević
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Vesna Todorčević: University of Belgrade, Faculty of Organizational Sciences

Chapter Chapter 6 in Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics, 2019, pp 131-146 from Springer

Abstract: Abstract Let G be a domain in ℝ n , $$\mathbb {R}^n,$$ f : G → ℝ n $$f: G \to \mathbb {R}^n$$ a harmonic map, and A $$\mathcal {A}$$ a class of self-homeomorphisms of G. We study in this chapter what can be said about the functions of the form f ∘ h , h ∈ A $$f \circ h, h \in \mathcal {A}$$ . For example, we show that if n = 2 and A $$\mathcal {A}$$ is the class of conformal maps, then the functions in this class are also harmonic. However, if A $$\mathcal {A}$$ is the class of harmonic maps, or quasiconformal harmonic maps, this statement is no longer true.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-22591-9_6

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DOI: 10.1007/978-3-030-22591-9_6

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