Stability Theorems in Geometry and Analysis, Softcover reprint of hardcover 1st ed. 1994
Mathematics and Its Applications Series, Vol. 304

Introduction. Möbius transformations. Integral representations and estimates for differentiable functions. Stability in Liouville's theorem on conformal mappings in space. Stability of isometric transformations of the space Rn. Stability in Darboux's theorem. Differential properties of mapping with bounded distortion and conformal mappings of Riemannian spaces.

1. Introduction.- 2. Möbius Transformations.- 3. Integral Representations and Estimates for Differentiable Functions.- 4. Stability in Liouville’s Theorem on Conformal Mappings in Space.- 5. Stability of Isometric Transformations of the Space ?n.- 6. Stability in Darboux’s Theorem.- 7. Differential Properties of Mappings with Bounded Distortion and Conformal Mappings of Riemannian Spaces.- References.

This monograph deals with the metric theory of spatial mappings and incorporates results in the theory of quasi-conformal, quasi-isomeric 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. Results obtained by others researching similar topics are mentioned, and a survey is given of publications treating relevant questions or involving the technique proposed.Introduction. Möbius transformations. Integral representations and estimates for differentiable functions. Stability in Liouville's theorem on conformal mappings in space. Stability of isometric transformations of the space Rn. Stability in Darboux's theorem. Differential