Tame Geometry with Application in Smooth Analysis

  • Authors
  • Yosef Yomdin
  • Georges Comte

Part of the Lecture Notes in Mathematics book series (LNM, volume 1834)

Table of contents

  1. Front Matter
    Pages N2-VIII
  2. Yosef Yomdin, Georges Comte
    Pages 1-22
  3. Yosef Yomdin, Georges Comte
    Pages 23-32
  4. Yosef Yomdin, Georges Comte
    Pages 33-45
  5. Yosef Yomdin, Georges Comte
    Pages 47-58
  6. Yosef Yomdin, Georges Comte
    Pages 59-73
  7. Yosef Yomdin, Georges Comte
    Pages 75-82
  8. Yosef Yomdin, Georges Comte
    Pages 83-98
  9. Yosef Yomdin, Georges Comte
    Pages 99-107
  10. Yosef Yomdin, Georges Comte
    Pages 109-130
  11. Yosef Yomdin, Georges Comte
    Pages 131-169
  12. Yosef Yomdin, Georges Comte
    Pages 171-186
  13. Back Matter
    Pages 187-189

About this book

Introduction

The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive. The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are "stable with respect to approximation", and can be imposed on smooth functions via polynomial approximation.

Keywords

Dimension Finite Smooth function algebraic geometry approximation boundary element method critical values of differentiable functions entropy functions geometry integral mapping proof semialgebraic sets theorem

Bibliographic information

  • DOI https://doi.org/10.1007/b94624
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-20612-5
  • Online ISBN 978-3-540-40960-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book