Semianalytic and subanalytic sets
Siciak's extremal function in complex and real analysis
The Siciak extremal function establishes an important link between polynomial approximation in several variables and pluripotential theory. This yields its numerous applications in complex and real analysis. Some of them can be found on a rich list drawn up by Klimek in his well-known monograph "Pluripotential Theory". The purpose of this paper is to supplement it by applications in constructive function theory.
Smooth ponts of p-adic subanalytic sets.
Smoothly equivalent real analytic proper G-mainfolds are subanalytically equivalent.
Some remarks on foliated S1 bundles.
Spectral geometry of semi-algebraic sets
The spectrum of the Laplace operator on algebraic and semialgebraic subsets in is studied and the number of small eigenvalues is estimated by the degree of .
Stokes' formula for stratified forms
A stratified form is a collection of forms defined on the strata of a stratification of a subanalytic set and satisfying a continuity property when we pass from one stratum to another. We prove that these forms satisfy Stokes' formula on subanalytic singular simplices.
Stratification of Real Analytic Mappings and Images.
Stratifications adapted to finite families of differential 1-forms (Pfaffian geometry - Part one).
A first part of a systematic presentation of Pfaffian geometry is given.
Stratifications distinguées comme outil en géometrie semi-analytique.
Stratifications et ensemble de non-cohérence d'un espace analytique rée.
Stratified Whitney jets and tempered ultradistributions on the subanalytic site
In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold . Then, we define stratified ultradistributions of Beurling and Roumieu type on . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to . Second, the tempered-stratified...
Subanalytic version of Whitney's extension theorem
For any subanalytic -Whitney field (k finite), we construct its subanalytic -extension to . Our method also applies to other o-minimal structures; e.g., to semialgebraic Whitney fields.
Sub-riemannian metrics : minimality of abnormal geodesics versus subanalyticity
Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity
We study sub-Riemannian (Carnot-Caratheodory) metrics defined by noninvolutive distributions on real-analytic Riemannian manifolds. We establish a connection between regularity properties of these metrics and the lack of length minimizing abnormal geodesics. Utilizing the results of the previous study of abnormal length minimizers accomplished by the authors in [Annales IHP. Analyse nonlinéaire 13, p. 635-690] we describe in this paper two classes of the germs of distributions (called 2-generating...
Sullivan's Local Euler Characteristic Theorem.
Supplement to the paper "Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices" (Ann. Polon. Math. 101 (2011), 275-291)
In IMUJ Preprint 2009/05 we investigated the quasianalytic perturbation of hyperbolic polynomials and symmetric matrices by applying our quasianalytic version of the Abhyankar-Jung theorem from IMUJ Preprint 2009/02, whose proof relied on a theorem by Luengo on ν-quasiordinary polynomials. But those papers of ours were suspended after we had become aware that Luengo's paper contained an essential gap. This gave rise to our subsequent article on quasianalytic perturbation theory, which developed,...
Sur la géométrie semi- et sous- analytique
Sur la triangulation des morphismes sous-analytiques
Sur les ensembles semi-analytiques avec conditions Gevrey au bord