Algébricité de germes analytiques.
An arc-analytic function with nondiscrete singular set
We construct an arc-analytic function (i.e. analytic on every real-analytic arc) in ℝ² which is analytic outside a nondiscrete subset of ℝ².
An elementary proof of the Briançon-Skoda theorem
We give an elementary proof of the Briançon-Skoda theorem. The theorem gives a criterionfor when a function belongs to an ideal of the ring of germs of analytic functions at ; more precisely, the ideal membership is obtained if a function associated with and is locally square integrable. If can be generated by elements,it follows in particular that , where denotes the integral closure of an ideal .
An interpolation theorem in toric varieties
In the spirit of a theorem of Wood, we give necessary and sufficient conditions for a family of germs of analytic hypersurfaces in a smooth projective toric variety to be interpolated by an algebraic hypersurface with a fixed class in the Picard group of .
An inverse mapping theorem for arc-analytic homeomorphisms
We show that a subanalytic map-germ (Rⁿ,0) → (Rⁿ,0) which is arc-analytic and bi-Lipschitz has an arc-analytic inverse.
Analytic and Polynominal Homomorphisms of Analytic Rings.
Analytic cell decomposition of sets definable in the structure
We prove that every set definable in the structure can be decomposed into finitely many connected analytic manifolds each of which is also definable in this structure.
Analytic curves in power series rings
Analytic deviation of ideals and intersection theory of analytic spaces.
Analytic disks with boundaries in a maximal real submanifold of
Let be a two dimensional totally real submanifold of class in . A continuous map of the closed unit disk into that is holomorphic on the open disk and maps its boundary into is called an analytic disk with boundary in . Given an initial immersed analytic disk with boundary in , we describe the existence and behavior of analytic disks near with boundaries in small perturbations of in terms of the homology class of the closed curve in . We also prove a regularity theorem...
Analytic rings
Analyticité séparée et prolongement analytique.
Analytische Hyperflächen mit vorgegebenen Singularitäten*.
Applications of Functional Analysis to the Solution of Power Series Equations.
Arc-analyticity and polynomial arcs
We relate the notion of arc-analyticity and the one of analyticity on restriction to polynomial arcs and we prove that in the subanalytic setting, these two notions coincide.
Are the Isolated Singularities of Complete Intersections Determined by Their Singular Subspaces?
Areas of Projections of Analytic Sets.
Artin-Large property for analytic manifolds of dimension two.
Attenuating the singularities of plurisubharmonic functions
We study the singularities of plurisubharmonic functions using methods from convexity theory. Analyticity theorems for a refined Lelong number are proved.