- Volume
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1 ISBN 9783034802086
Description
The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the book also is unified by geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience.
Table of Contents
Preface.- Basic Terms and Notation.- Part 1. Classical Extension-Trace Theorems and Related Results.- Chapter 1. Continuous and Lipschitz Functions.- Chapter 2. Smooth Functions on Subsets of Rn.- Part 2. Topics in Geometry of and Analysis on Metric Spaces.- Chapter 3. Topics in Metric Space Theory.- Chapter 4. Selected Topics in Analysis on Metric Spaces.- Chapter 5. Lipschitz Embedding and Selections.- Bibliography.- Index.
- Volume
-
2 ISBN 9783034802116
Description
The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the book also is unified by geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience.
Table of Contents
Part 3. Lipschitz Extensions from Subsets of Metric Spaces.- Chapter 6. Extensions of Lipschitz Maps.- Chapter 7. Simultaneous Lipschitz Extensions.- Chapter 8. Linearity and Nonlinearity.- Part 4. Smooth Extension and Trace Problems for Functions on Subsets of Rn.- Chapter 9. Traces to Closed Subsets: Criteria, Applications.- Chapter 10. Whitney Problems.- Bibliography.- Index.
by "Nielsen BookData"
