Methods of Geometric Analysis in Extension and Trace Problems

Volume 2

  • Alexander Brudnyi
  • Yuri Brudnyi

Part of the Monographs in Mathematics book series (MMA, volume 103)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Lipschitz Extensions from Subsets of Metric Spaces

    1. Front Matter
      Pages 1-1
    2. Alexander Brudnyi, Yuri Brudnyi
      Pages 3-48
    3. Alexander Brudnyi, Yuri Brudnyi
      Pages 49-116
    4. Alexander Brudnyi, Yuri Brudnyi
      Pages 117-151
  3. Smooth Extension and Trace Problems for Functions on Subsets of ℝ n

    1. Front Matter
      Pages 153-153
    2. Alexander Brudnyi, Yuri Brudnyi
      Pages 155-240
    3. Alexander Brudnyi, Yuri Brudnyi
      Pages 241-381
  4. Back Matter
    Pages 383-414

About this book


This is the second 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.


geometric analysis metric space theory

Authors and affiliations

  • Alexander Brudnyi
    • 1
  • Yuri Brudnyi
    • 2
  1. 1., Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2., Mathematics DepartmentTechnion - Israel Institute of TechnologHaifaIsrael

Bibliographic information