Characteristic varieties and vanishing cycles.
Characterization of global Phragmén-Lindelöf conditions for algebraic varieties by limit varieties only
For algebraic surfaces, several global Phragmén-Lindelöf conditions are characterized in terms of conditions on their limit varieties. This shows that the hyperbolicity conditions that appeared in earlier geometric characterizations are redundant. The result is applied to the problem of existence of a continuous linear right inverse for constant coefficient partial differential operators in three variables in Beurling classes of ultradifferentiable functions.
Chebyshev and Robin constants on algebraic curves
We define directional Robin constants associated to a compact subset of an algebraic curve. We show that these constants satisfy an upper envelope formula given by polynomials. We use this formula to relate the directional Robin constants of the set to its directional Chebyshev constants. These constants can be used to characterize algebraic curves on which the Siciak-Zaharjuta extremal function is harmonic.
Closure Theorem for Partially Semialgebraic Sets
In 1988 it was proved by the first author that the closure of a partially semialgebraic set is partially semialgebraic. The essential tool used in that proof was the regular separation property. Here we give another proof without using this tool, based on the semianalytic L-cone theorem (Theorem 2), a semianalytic analog of the Cartan-Remmert-Stein lemma with parameters.
Compact Varieties of Surjective Holomorphic Endomorphisms.
Compactifications kähleriennes de voisinages ouverts de cycles géométriquement positifs
Complete Intersections in Stein Manifolds.
Complete locally pluripolar sets.
Complex characteristic coordinates and tangential Cauchy-Riemann equations
Complexité et géométrie réelle
Concavity Theorems.
Construction d’hypersurfaces irréductibles avec lieu singulier donné dans
Étant donné un ensemble analytique de codimension dans , nous construisons des hypersurfaces irréductibles de lieu singulier , avec contrôle de la croissance. À partir d’un contre-exemple au problème de Bezout transcendant, dû à M. Cornalba et B. Shiffman, nous montrons l’existence d’une courbe irréductible d’ordre 0 dans , dont le lieu singulier est d’ordre infini. Nous étudions également en application certaines propriétés arithmétiques de l’anneau de convolution
Continuing Analytic Sets Across IRn.
Continuity of intersection of analytic sets
Convergence of holomorphic chains
We endow the module of analytic p-chains with the structure of a second-countable metrizable topological space.
Correction to "C*-actions".
Courants algébriques et courants de Liouville
We define in ℂⁿ the concepts of algebraic currents and Liouville currents, thus extending the concepts of algebraic complex subsets and Liouville subsets. After having shown that every algebraic current is Liouville, we characterize those positive closed currents on ℂⁿ which are algebraic. Let T be a closed positive current on ℂⁿ. We give sufficient conditions, relating to the growth of the projective mass of T, so that T is Liouville. These results generalize those previously obtained by N. Sibony...
Densité des ensembles semi-pfaffiens
Densité des fonctions plurisousharmoniques
Der Satz von Remmert-Stein in der nichtarchimedischen Funktionentheorie.