1.

Record Nr.

UNINA9910144619803321

Autore

Yomdin Yosef

Titolo

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

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004

ISBN

3-540-40960-2

Edizione

[1st ed. 2004.]

Descrizione fisica

1 online resource (CC, 190 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1834

Disciplina

515.42

Soggetti

Geometry, Algebraic

Measure theory

Functions of real variables

Functions of complex variables

Algebraic Geometry

Measure and Integration

Real Functions

Several Complex Variables and Analytic Spaces

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references (pages 173-186).

Nota di contenuto

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.

Sommario/riassunto

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.