Quasiconformal and Quasiregular Harmonic Mappings

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

Chapter Chapter 2 in Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics, 2019, pp 5-56 from Springer

Abstract: Abstract In this chapter we build the foundation for the work that comes in the rest of the book. We begin with the definition of two conformal invariants, the modulus of a curve family and the capacity of a condenser, which are two closely related notions. These tools enable us to define quasiconformal and quasiregular mappings which are the basic classes of mappings to be studied. Several examples of quasiconformal mappings are given illustrating the importance of this class of functions and their role in Geometric Function Theory. Moduli of continuity of harmonic mappings, which are either quasiconformal or quasiregular at the same time, are considered and some sharp estimates are given for all dimensions n ≥ 2. In particular, we study the case of Lipschitz continuity of mappings defined in the unit ball.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-22591-9_2

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DOI: 10.1007/978-3-030-22591-9_2

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