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Quasi-Nearly Subharmonic Functions and QC Mappings

  • Vesna Todorčević
Chapter
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Abstract

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

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vesna Todorčević
    • 1
    • 2
  1. 1.Faculty of Organizational SciencesUniversity of BelgradeBelgradeSerbia
  2. 2.Mathematical InstituteSerbian Academy of Sciences and ArtsBelgradeSerbia

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