Publisher's Synopsis
This monograph deals with the metric theory of spatial mappings and incorporates results in the theory of quasi-conformal, quasi-isometric and other mappings.;The main subject is the study of the stability problem in Liouville's theorem on conformal mappings in space, which is representative of a number of problems on stability for transformation classes. To enable this investigation a wide range of mathematical tools has been developed which incorporate the calculus of variation, estimates for differential operators like Korn inequalities, properties of functions with bounded mean oscillation, etc.;Results obtained by others researching similar topics are mentioned, and a survey is given of publications treating relevant questions or involving the technique proposed.;This volume should be of interest to graduate students and researchers interested in geometric function theory.
