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MARC 21

Methods of Geometric Analysis in Extension and Trace Problems: Volume 1
Tag	Description
020	$a9783034802093
082	$a515.7
099	$aOnline Resource: Springer
100	$aBrudnyi, Alexander.
245	$aMethods of Geometric Analysis in Extension and Trace Problems$h[EBook]$bVolume 1$cby Alexander Brudnyi, Yuri Brudnyi.
260	$aBasel$bSpringer Basel$c2012.
300	$aXXIII, 560 pages : 11 illus.$bonline resource.
336	$atext
338	$aonline resource
440	$aMonographs in Mathematics ;$v102
505	$aPreface -- 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.
520	$aThis 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
700	$aBrudnyi, Yuri.$eauthor.
710	$aSpringerLink (Online service)
830	$aMonographs in Mathematics ;$v102
856	$uhttp://dx.doi.org/10.1007/978-3-0348-0209-3