Recent connections and applications of planar quasiconformal mappings. (English) Zbl 0908.30019

Balog, A. (ed.) et al., European congress of mathematics (ECM), Budapest, Hungary, July 22–26, 1996. Volume I. Basel: Birkhäuser. Prog. Math. 168, 36-51 (1998).
The paper is devoted to connections of plane quasiconformal (QC) mappings to holomorphic deformations, complex dynamics, regularity and removability properties of solutions of elliptic PDE’s, singular integrals and the Beurling transformation. Recent applications to the mathematical theory of composite materials are also dealt with. In many cases, the author points out the influence [K. Astala, Acta Math. 173, No. 1, 37-60 (1994; Zbl 0815.30015)] the best integrability exponent of the derivative of a QC mapping to the problem area in question.
For the entire collection see [Zbl 0893.00027].


30C62 Quasiconformal mappings in the complex plane


Zbl 0815.30015