Methods of geometric analysis in extension and trace problems
 Responsibility
 Alexander Brudnyi, Yuri Brudnyi.
 Imprint
 [Basel, Switzerland] : Birkhäuser, c2012.
 Physical description
 2 v. : ill. ; 24 cm.
 Series
 Monographs in mathematics ; v. 102103.
Access
Available online
Science Library (Li and Ma)
Stacks
Library has: v.12
Call number  Status 

QA611.3 .B78 2010 V.1  Unknown 
QA611.3 .B78 2010 V.2  Unknown 
More options
Creators/Contributors
 Author/Creator
 Brudnyi, Alexander.
 Contributor
 Brudnyĭ, I͡U. A.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 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.
 (source: Nielsen Book Data)9783034802116 20160607
 Preface. Basic Terms and Notation. Part 1. Classical ExtensionTrace 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.
 (source: Nielsen Book Data)9783034802086 20160607
 Publisher's Summary
 The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extensiontrace 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.
(source: Nielsen Book Data)9783034802086 20160607
Subjects
Bibliographic information
 Publication date
 2012
 Series
 Monographs in mathematics ; v. 102103
 ISBN
 9783034802086 (v. 1 : acidfree paper)
 3034802080 (v. 1 : acidfree paper)
 9783034802116 (v. 2 : acidfree paper)
 3034802110 (v. 2 : acidfree paper)
 9783034802093 (v. 1 : eISBN)
 3034802099 (v. 1 : eISBN)
 9783034802123 (v. 2 : eISBN)
 3034802129 (v. 2 : eISBN)