Tame Geometry with Application in Smooth Analysis - Yosef Yomdin, Georges Comte

Tame Geometry with Application in Smooth Analysis

Buch | Softcover
CC, 190 Seiten
2004 | 2004
Springer Berlin (Verlag)
978-3-540-20612-5 (ISBN)
48,14 inkl. MwSt

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.

From the contents:
Preface.- Introduction and Content.- Entropy.- Multidimensional Variations.- Semialgebraic and Tame Sets.- Some Exterior Algebra.- Behavior of Variations under Polynomial Mappings.- Quantitative Transversality and Cuspidal Values for Polynomial Mappings.- Mappings of Finite Smoothness.- Some Applications and Related Topics.- Glossary.- References.

Erscheint lt. Verlag 23.1.2004
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo CC, 190 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 305 g
Themenwelt Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte 28A75, 14Q20, 14P10, 26B5, 26B15, 32S15 • Algebraic Geometry • Approximation • Boundary element method • critical values of differentiable functions • Dimension • Entropy • Finite • Functions • Geometry • Glättung • Integral • mapping • Proof • semialgebraic sets • Smooth function • Theorem
ISBN-10 3-540-20612-4 / 3540206124
ISBN-13 978-3-540-20612-5 / 9783540206125
Zustand Neuware
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