Local algebraicity of analytic sets.
Local analytic invariants
Local analytic rings
Local Complex Foliation of Real Submanifolds.
Local generalizations of Lefschetz-Zariski theorems.
Local geometry of zero sets of holomorphic functions near the torus.
Local semianalytic geometry.
Lokale Algebra und lokale Geometrie.
l-Platte Funktionen auf semianalytischen Mengen.
Markov's Inequality and C Functions on Sets with Polynomial Cusps.
Michael's theorem for Lipschitz cells in o-minimal structures
A version of Michael's theorem for multivalued mappings definable in o-minimal structures with M-Lipschitz cell values (M a common constant) is proven. Uniform equi-LCⁿ property for such families of cells is checked. An example is given showing that the assumption about the common Lipschitz constant cannot be omitted.
Minimal generation of basic open semianalytic sets.
...-Modules on Supermanifolds.
Monodromy of functions defined on isolated singularities of complete intersections
Multiplicity and the Lojasiewicz exponent
Multiplicity and the Łojasiewicz exponent
We give a formula for the multiplicity of a holomorphic mapping , m > n, at an isolated zero, in terms of the degree of an analytic set at a point and the degree of a branched covering. We show that calculations of this multiplicity can be reduced to the case when m = n. We obtain an analogous result for the local Łojasiewicz exponent.
Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods
We give a state-of-the-art survey of investigations concerning multivariate polynomial inequalities. A satisfactory theory of such inequalities has been developed due to applications of both the Gabrielov-Hironaka-Łojasiewicz subanalytic geometry and pluripotential methods based on the complex Monge-Ampère operator. Such an approach permits one to study various inequalities for polynomials restricted not only to nice (nonpluripolar) compact subsets of ℝⁿ or ℂⁿ but also their versions for pieces...
Nicht-ausgeartete reguläre Überlagerungen.
Noethérianité de certaines algèbres de fonctions analytiques et applications
Let be a real-analytic submanifold and H(M) the algebra of real analytic functions on M. If K ⊂ M is a compact subset we consider ; is a multiplicative subset of . Let be the localization of H(M) with respect to . In this paper we prove, first, that is a regular ring (hence noetherian) and use this result in two situations: 1) For each open subset , we denote by O(Ω) the subalgebra of H(Ω) defined as follows: f ∈ O(Ω) if and only if for all x ∈ Ω, the germ of f at x, , is algebraic...
Normalisation des champs de vecteurs holomorphes