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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
