Holomorphic flows and complex structures on products of odd dimensional spheres.
Holomorphic foliations by curves on with non-isolated singularities
Let be a holomorphic foliation by curves on . We treat the case where the set consists of disjoint regular curves and some isolated points outside of them. In this situation, using Baum-Bott’s formula and Porteuos’theorem, we determine the number of isolated singularities, counted with multiplicities, in terms of the degree of , the multiplicity of along the curves and the degree and genus of the curves.
Holomorphic framings for projections in a Banach algebra.
Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces
We introduce a decomposition of holomorphic functions on Fréchet spaces which reduces to the Taylor series expansion in the case of Banach spaces and to the monomial expansion in the case of Fréchet nuclear spaces with basis. We apply this decomposition to obtain examples of Fréchet spaces E for which the τ_{ω} and τ_{δ} topologies on H(E) coincide. Our result includes, with simplified proofs, the main known results-Banach spaces with an unconditional basis and Fréchet nuclear spaces with DN [2,...
Holomorphic functions and subelliptic heat kernels over Lie groups
Holomorphic functions of fast growth on submanifolds of the domain
We construct a function f holomorphic in a balanced domain D in such that for every positive-dimensional subspace Π of , and for every p with 1 ≤ p < ∞, is not -integrable on Π ∩ D.
Holomorphic functions on Fréchet spaces with Schauder basis.
Holomorphic functions on locally convex topological vector spaces. II. Pseudo convex domains
In this article we discuss the relationship between domains of existence domains of holomorphy, holomorphically convex domains, pseudo convex domains, in the context of locally convex topological vector spaces. By using the method of Hirschowitz for and the method used for Banach spaces with a basis we prove generalisations of the Cartan-Thullen-Oka-Norguet-Bremmerman theorem for finitely polynomially convex domains in a variety of locally convex spaces which include the following:1) -projective...
Holomorphic functions with singularities on algebraic sets.
Holomorphic generators of some ideals in
Holomorphic group actions with few compact orbits
Holomorphic group actions with many compact orbits.
Holomorphic immersions between compact hyperbolic space forms.
Holomorphic isometries of Cartan domains of type one
Holomorphic isometries for the Kobayashi metric of a class of Cartan domains are characterized.
Holomorphic Lagrangian bundles over flag manifolds.
Holomorphic line bundles and divisors on a domain of a Stein manifold
Let be an open set of a Stein manifold of dimension such that for . We prove that is Stein if and only if every topologically trivial holomorphic line bundle on is associated to some Cartier divisor on .
Holomorphic line bundles on a domain of a two-dimensional Stein manifold
Let D be an open subset of a two-dimensional Stein manifold S. Then D is Stein if and only if every holomorphic line bundle L on D is the line bundle associated to some (not necessarily effective) Cartier divisor 𝔡 on D.
Holomorphic Lipschitz functions and application to the -problem
Holomorphic Lipschitz functions in balls.
Holomorphic mapping of annuli in and the associated extremal function