A note on Rosay's paper
We give a simplified proof of J. P. Rosay's result on plurisubharmonicity of the envelope of the Poisson functional [10].
A note on singularities at infinity of complex polynomials
Let f be a complex polynomial. We relate the behaviour of f “at infinity” to the sheaf of vanishing cycles of the family of projective closures of fibres of f. We show that the absence of such cycles: (i) is equivalent to a condition on the asymptotic behaviour of gradient of f known as Malgrange’s Condition, (ii) implies the -triviality of f. If the support of sheaf of vanishing cycles of is a finite set, then it detects precisely the change of the topology of the fibres of f. Moreover, in...
A note on the Cauchy-Bochner formula for a class of Beurling ultradistributions
A note on the discriminant of a space curve.
A note on the extension of analytic functions off real analytic subsets.
Let X be a closed analytic subset of an open subset Omega of Rn. We look at the problem of extending functions from X to Omega.
A note on the holomorphic invariants of Tian-Zhu.
A note on the Hörmander, Donnelly-Fefferman, and Berndtsson L²-estimates for the ∂̅-operator
We give upper and lower bounds for constants appearing in the L²-estimates for the ∂̅-operator due to Donnelly-Fefferman and Berndtsson.
A Note on the kernel of the ...-Neumann operator on strongly pseudoconvex domains.
A note on the Kobayashi pseudodistance and the tautness of holomorphic fiber bundles
We show a relation between the Kobayashi pseudodistance of a holomorphic fiber bundle and the Kobayashi pseudodistance of its base. Moreover, we prove that a holomorphic fiber bundle is taut iff both the fiber and the base are taut.
A note on the Lawrence-Krammer-Bigelow representation.
A note on the Nullstellensatz for c-holomorphic functions
We begin this article with a graph theorem and a kind of Nullstellensatz for weakly holomorphic functions. This yields a general Nullstellensatz for c-holomorphic functions on locally irreducible sets. In Section 2 some methods of Płoski-Tworzewski permit us to prove an effective Nullstellensatz for c-holomorphic functions in the case of a proper intersection with the degree of the intersection cycle as exponent. We also extend this result to the case of isolated improper intersection, generalizing...
A note on the regularity of the degenerate complex Monge-Ampère equation
We prove the almost regularity of the degenerate complex Monge-Ampère equation in a special case.
A notion of boundedness for hyperfunctions and Massera type theorems
For some classes of periodic linear ordinary differential equations and functional equations, it is known that the existence of a bounded solution in the future implies the existence of a periodic solution. In order to think on such phenomena for hyperfunction solutions to linear functional equations, we introduced a notion of bounded hyperfunctions, and translated the problems into the problems on analytic solutions to some equations in complex domains. In this article, after...
A notion of extremal analytic discs related to interpolation in the ball.
A p-adic Nevanlinna-Diophantine correspondence
A Peak Set of Hausdorff Dimension 2n? 1 for the Algebra A(D) in the Boundary of a Domain D with C°°-Boundary in Cn.
A pointwise growth estimate for analytic functions in tubes.
A precise result on the boundary regularity of biholomorphic mappings (Erratum).
A Precise Result on the Boundary Regularity of Biholomorphic Mappings.
A Priori Estimates and a Liouvielle Theorem for Complex Monge-Ampère Equations.