E. E. Levi convexity and the Hans Lewy problem. Part I : reduction to vanishing theorems
E. E. Levi convexity and the Hans Lewy problem. Part II : vanishing theorems
Each homotopically homogeneous tube in has an affine-homogeneous base.
Each Non-Zero Convolution Operator on the Entire Functions Admits a Continuous Linear Right Inverse.
Earthquakes are analytic.
Éclatement des coefficients des séries entières et deux théorème des Gabrielov.
Éclatements quasi homogènes
Edge-of-the-wedge theorem for elliptic systems
Editorial statement on the paper: The Corona theorem for the ball and polydisc.
Effective formulas for complex geodesics in generalized pseudoellipsoids with applications
We introduce a class of generalized pseudoellipsoids and we get formulas for their complex geodesics in the convex case. Using these formulas we get a description of automorphisms of the pseudoellipsoids. We also solve the problem of biholomorphic equivalence of convex complex ellipsoids without any sophisticated machinery.
Effective formulas for invariant functions - case of elementary Reinhardt domains
We find effective formulas for the invariant functions, appearing in the theory of several complex variables, of the elementary Reinhardt domains. This gives us the first example of a large family of domains for which the functions are calculated explicitly.
Effective Formulas for the carathéodory distance.
Effective freeness and point separation for adjoint bundles.
Effective local finite generation of multiplier ideal sheaves
Let be a psh function on a bounded pseudoconvex open set , and let be the associated multiplier ideal sheaves, . Motivated by global geometric issues, we establish an effective version of the coherence property of as . Namely, given any , we estimate the asymptotic growth rate in of the number of generators of over , as well as the growth of the coefficients of sections in with respect to finitely many generators globally defined on . Our approach relies on proving asymptotic integral...
Effective Nullstellensatz for arbitrary ideals
Let be polynomials in variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials such that . The effective versions of this result bound the degrees of the in terms of the degrees of the . The aim of this paper is to generalize this to the case when the are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.
Effectiveness of similar sets of polynomials of two complex variables in polycylinders and in Faber regions.
Eigenvaluations
Ein allgemeines Kriterium für das formale Prinzip.
Ein Approximationssatz auf streng pseudokonvexen Gebieten.
Ein Approximationssatz für holomorphe Funktionen auf nicht-kompakte Riemannschen Flächen.