# zbMATH — the first resource for mathematics

Special functions of quasiconformal theory. (English) Zbl 0686.30015
Two basic functions of the theory of quasiconformal mappings in the n- space (n$$\geq 2)$$, the capacities of the Grötzsch and Teichmüller rings, are discussed in this paper. Several functional inequalities of these special functions are given for all dimensions $$n\geq 2$$, even though in the higher-dimensional case $$n\geq 3$$ neither explicit expressions nor functional identities are known. The authors develop a systematic theory of these special functions in the n-space, which contains several new results even for $$n=2$$. A list of open questions is given at the end of the paper.
Reviewer: Li Zhong

##### MSC:
 30C62 Quasiconformal mappings in the complex plane 33E05 Elliptic functions and integrals 33E99 Other special functions
##### Keywords:
extremal length method