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Catalogue Information
Field name	Details
Dewey Class	515.7
Title	Methods of Geometric Analysis in Extension and Trace Problems ([EBook]) : Volume 1 / by Alexander Brudnyi, Yuri Brudnyi.
Author	Brudnyi, Alexander
Added Personal Name	Brudnyi, Yuri
Other name(s)	SpringerLink (Online service)
Publication	Basel : Springer Basel , 2012.
Physical Details	XXIII, 560 pages : 11 illus. : online resource.
Series	Monographs in mathematics ; 102
ISBN	9783034802093
Summary Note	This is the first of a two-volume work presenting 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 the 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 work is also unified by the 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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-0348-0209-3
Links to Related Works	Subject References: Functional Analysis . Mathematics . Authors: author . Brudnyi, Alexander . Brudnyi, Yuri . Corporate Authors: SpringerLink (Online service) . Series: Monographs in mathematics . Classification: 515.7 . 515.7 (DDC 23) .

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Methods of Geometric Analysis in Extension and Trace Problems: Volume 1

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