Lecture Notes in Mathematics

Tame Geometry with Application in Smooth Analysis

Authors: Yomdin, Yosef, Comte, Georges

Free Preview

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-540-40960-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-540-20612-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this book

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.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-540-40960-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-540-20612-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Loading...

Bibliographic Information

Bibliographic Information
Book Title
Tame Geometry with Application in Smooth Analysis
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1834
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-40960-1
DOI
10.1007/b94624
Softcover ISBN
978-3-540-20612-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
CC, 190
Topics