Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1834)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
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.
Bibliographic Information
Book Title: Tame Geometry with Application in Smooth Analysis
Authors: Yosef Yomdin, Georges Comte
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b94624
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2004
Softcover ISBN: 978-3-540-20612-5Published: 23 January 2004
eBook ISBN: 978-3-540-40960-1Published: 07 February 2004
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: CC, 190
Topics: Algebraic Geometry, Measure and Integration, Real Functions, Several Complex Variables and Analytic Spaces