Distortion of quasiconformal mappings with identity boundary values

Abstract Teichm¨uller’s classical mapping problem for plane domains concerns finding a lower bound for the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise fixed, maps the domain onto itself and maps a given point of the domain to another given point of the domain. For a domain D ⊂ Rn, n > 2, we consider the class of all K-quasiconformal maps of…