Ebook: Stability Theorems in Geometry and Analysis

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.

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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.

Content:
Front Matter....Pages i-xi
Introduction....Pages 1-62
M?bius Transformations....Pages 63-105
Integral Representations and Estimates for Differentiable Functions....Pages 106-203
Stability in Liouville’s Theorem on Conformal Mappings in Space....Pages 204-299
Stability of Isometric Transformations of the Space ? n ....Pages 300-335
Stability in Darboux’s Theorem....Pages 336-355
Differential Properties of Mappings with Bounded Distortion and Conformal Mappings of Riemannian Spaces....Pages 356-382
Back Matter....Pages 383-394

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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.

Content:
Front Matter....Pages i-xi
Introduction....Pages 1-62
M?bius Transformations....Pages 63-105
Integral Representations and Estimates for Differentiable Functions....Pages 106-203
Stability in Liouville’s Theorem on Conformal Mappings in Space....Pages 204-299
Stability of Isometric Transformations of the Space ? n ....Pages 300-335
Stability in Darboux’s Theorem....Pages 336-355
Differential Properties of Mappings with Bounded Distortion and Conformal Mappings of Riemannian Spaces....Pages 356-382
Back Matter....Pages 383-394
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