The symmetric pluricomplex Green function
The symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains
We prove that the symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains.
The sympletic nature of the space of projective connections on Riemann surfaces.
The theorem of Barth-Lefschetz as a consequence of Le Potier's vanishing theorem.
The theorem of Forelli for holomorphic mappings into complex spaces
Generalizations of the theorem of Forelli to holomorphic mappings into complex spaces are given.
The theorem of the complement for a quasi subanalytic set
Let X ⊂ (ℝⁿ,0) be a germ of a set at the origin. We suppose X is described by a subalgebra, Cₙ(M), of the algebra of germs of functions at the origin (see 2.1). This algebra is quasianalytic. We show that the germ X has almost all the properties of germs of semianalytic sets. Moreover, we study the projections of such germs and prove a version of Gabrielov’s theorem.
The theorems of Glicksberg and Hurwitz for holomorphic maps in complex Banach spaces
General versions of Glicksberg's theorem concerning zeros of holomorphic maps and of Hurwitz's theorem on sequences of analytic functions is extended to infinite dimensional Banach spaces.
The three point pick problem on the bidisk.
The Thullen type extension theorem for holomorphic vector bundles with L2-bounds on curvature.
The topology of holomorphic flows with singularity
The topology of Stein CR manifolds and the Lefschetz theorem
Necessary topological conditions are given for the closed CR embedding of a CR manifold into a Stein manifold or into a complex projective space.
The Torelli map at the boundary of the Schottky space.
The trace formula for equivariant D-modules and perverse sheaves.
The transcendence of certain quasi-periods associated with abelian functions in two variables
The transfinite diameter of the real ball and simplex
We calculate the transfinite diameter for the real unit ball and the real unit simplex
The trivial locus of an analytic map germ
We prove: For a local analytic family of analytic space germs there is a largest subspace in such that the family is trivial over . Moreover the reduction of equals the germ of those points in for which is isomorphic to the special fibre .
The ultra-distributions of exponential type of J. Sebastião e Silva
The union problem on complex manifolds.
The use of conjugate convex functions in complex analysis
The use of D-modules to study exponential polynomials
This is a summary of recent work where we introduced a class of D-modules adapted to study ideals generated by exponential polynomials.