Stability Theorems in Geometry and Analysis / Edition 1

by Yu.G. Reshetnyak

Overview

This is one of the first monographs to deal 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 will be of great value to graduate students and researchers interested in geometric function theory.

Product Details

ISBN-13:	9780792331186
Publisher:	Springer Netherlands
Publication date:	09/30/1994
Series:	Mathematics and Its Applications , #304
Edition description:	1994
Pages:	394
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

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.