A Construction of Inner Functions on the Unit Ball in Cp.
A Construction of Normal Forms for Weakly Pseudoconvex CR Manifolds in ...2.
A construction of the Deligne-Mumford orbifold
A constructive proof of the composition rule for Taylor's functional calculus
We give a new constructive proof of the composition rule for Taylor's functional calculus for commuting operators on a Banach space.
A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions
We present a constructive proof of the fact that the set of algebraic Pfaff equations without algebraic solutions over the complex projective plane is dense in the set of all algebraic Pfaff equations of a given degree.
A Contraction of S U (2) to the Heisenberg Group.
A converse to the Andreotti-Grauert theorem
The goal of this paper is to show that there are strong relations between certain Monge-Ampère integrals appearing in holomorphic Morse inequalities, and asymptotic cohomology estimates for tensor powers of holomorphic line bundles. Especially, we prove that these relations hold without restriction for projective surfaces, and in the special case of the volume, i.e. of asymptotic -cohomology, for all projective manifolds. These results can be seen as a partial converse to the Andreotti-Grauert...
A correction to and a remark on our paper "Remarks on the proof of a generalized Hartogs Lemma" (Ann. Polon. Math. 70 (1998), 43-47)
A Counterexample for the Levi Problem for the Branched Riemann Domains over Cn.
A counter-example in singular integral theory
An improvement of a lemma of Calderón and Zygmund involving singular spherical harmonic kernels is obtained and a counter-example is given to show that this result is best possible. In a particular case when the singularity is O(|log r|), let and suppose f vanishes outside of a compact subset of , N ≥ 2. Also, let k(x) be a Calderón-Zygmund kernel of spherical harmonic type. Suppose f(x) = O(|log r|) as r → 0 in the -sense. Set . Then F(x) = O(log²r) as r → 0 in the -sense, 1 < p < ∞....
A Counterexample to Artin Approximation With Respect to Subrings.
A counterexample to subanalyticity of an arc-analytic function
We construct an arc-analytic function (i.e. a function analytic on each analytic arc) whose graph is not subanalytic.
A counterexample to the regularity of the degenerate complex Monge-Ampère equation
We modify an example due to X.-J. Wang and obtain some counterexamples to the regularity of the degenerate complex Monge-Ampère equation on a ball in ℂⁿ and on the projective space ℙⁿ.
A Counterexample to the Strong Subadditivity of Extremal Plurisubharmonic Functions.
A criterion for algebraicity of certain analytic elliptic surfaces.
A Criterion for Flatness of Hodge Bundles over Curves and Geometrie Applications.
A criterion for the existence of a flat connection on a parabolic vector bundle.
A Criterion for the Neumann Type Problem over a Differential Complex on a Strongly Pseudo Convex Domain.
A cut-off theorem for plurisubharmonic currents.
A decomposition of a set definable in an o-minimal structure into perfectly situated sets
A definable subset of a Euclidean space X is called perfectly situated if it can be represented in some linear system of coordinates as a finite union of (graphs of) definable 𝓒¹-maps with bounded derivatives. Two subsets of X are called simply separated if they satisfy the Łojasiewicz inequality with exponent 1. We show that every closed definable subset of X of dimension k can be decomposed into a finite family of closed definable subsets each of which is perfectly situated and such that any...