Monographs in Mathematics

Methods of Geometric Analysis in Extension and Trace Problems

Volume 2

Authors: Brudnyi, Alexander, Technion R&D Foundation Ltd, Prof. Yuri Brudnyi

  • Covers the development of the area from the first half of the 20th century to the last decade
  • Well suited for self-study
  • Necessary facts presented mostly with detailed proofs
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  • ISBN 978-3-0348-0212-3
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Hardcover $149.00
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Softcover $149.00
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  • ISBN 978-3-0348-0339-7
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About this book

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.

Reviews

“Book under review is enormous in scope and contains most of the old and current results on extension problems. Many of the theorems appear here for the first time in book form. The book is self-contained, and the detailed arguments make it accessible to a wide audience, especially graduate students interested in getting into the subject. … It will become a standard reference in the subject, and it deserves a spot in the library.” (Garving K. Luli, Bulletin of the American Mathematical Society, Vol. 53 (1), January, 2016)

“The two-volume monograph is divided into ten chapters, with five chapters in each volume. … Volume II reports on the recent progress in the area of the extension and trace problems. … the book successfully conveys the authors’ coherent vision for the subject, with the emphasis on linear extension operators, finiteness properties, and the treatment of extension via selection. It is certain to become a standard reference in the field.” (Leonid V. Kovalev, Mathematical Reviews, Issue 2012 j)

Table of contents (5 chapters)

  • Extensions of Lipschitz Maps

    Brudnyi, Alexander (et al.)

    Pages 3-48

  • Simultaneous Lipschitz Extensions

    Brudnyi, Alexander (et al.)

    Pages 49-116

  • Linearity and Nonlinearity

    Brudnyi, Alexander (et al.)

    Pages 117-151

  • Traces to Closed Subsets:Criteria, Applications

    Brudnyi, Alexander (et al.)

    Pages 155-240

  • Whitney Problems

    Brudnyi, Alexander (et al.)

    Pages 241-381

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0212-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-0348-0211-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-0348-0339-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Methods of Geometric Analysis in Extension and Trace Problems
Book Subtitle
Volume 2
Authors
Series Title
Monographs in Mathematics
Series Volume
103
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-0212-3
DOI
10.1007/978-3-0348-0212-3
Hardcover ISBN
978-3-0348-0211-6
Softcover ISBN
978-3-0348-0339-7
Series ISSN
1017-0480
Edition Number
1
Number of Pages
XX, 416
Topics