Related papers: On Hilbert-Hartogs manifolds

For geometrically finite hyperbolic manifolds $\Gamma\backslash H^{n+1}$, we prove the meromorphic extension of the resolvent of Laplacian, Poincar\'e series, Einsenstein series and scattering operator to the whole complex plane. We also…

Replaced by a shorter version which appeared in press.

We give density results for automorphic representations of Hilbert modular groups. In particular, we show that there are infinitely many automorphic representations that have a prescribed discrete series factor at some (but not all) real…

We extend to the context of algebraic groups a classic result on extensions of abstract groups relating the set of isomorphism classes of extensions of $G$ by $H$ with that of extensions of $G$ by the center $Z$ of $H$. The proof should be…

We prove that proper pseudo-holomorphic maps between strictly pseudoconvex regions in almost complex manifolds extend to the boundary. The key point is that the Jacobian is far from zero near the boundary, and the proof is mainly based on…

We prove a general result about the geometry of holomorphic line bundles over Kahler manifolds.

We study the problem of holomorphic extension of a smooth CR mapping from a real analytic hypersurface to a real algebraic set in complex spaces of different dimensions.

We study a class of holomorphic matrix models. The integrals are taken over middle dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a…

In this paper, we study the representation of orthogonally additive mappings acting on Hilbert $C^*$-modules and Hilbert $H^*$-modules. One of our main results shows that every continuous orthogonally additive mapping $f$ from a Hilbert…

We construct large families of harmonic morphisms which are holomorphic with respect to Hermitian structures by finding heierarchies of Weierstrass-type representations. This enables us to find new examples of complex-valued harmonic…

In terms of dilatations, it is proved a series of criteria for continuous and homeomorphic extension to the boundary of mappings with finite distortion between regular domains on the Riemann surfaces

This is a survey on recent results on the Loewner theory in one and several complex manifolds

We develop representations for bicomplex-valued functions in Hardy classes that generalize the complex holomorphic Hardy spaces. Using these representations, we show these functions have boundary values in the sense of distributions that…

In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.

We study the degeneracy of holomorphic mappings tangent to holomorphic foliations on projective manifolds. Using Ahlfors currents in higher dimension, we obtain several strong degeneracy statements.

In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.

We associate to a multiple polylogarithm a holomorphic 1-form on the universal abelian cover of its domain. We relate the 1-forms to the symbol and variation matrix and show that the 1-forms naturally define a lift of the variation of mixed…

We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…

Let $B^n$ be the $n$-dimensional unit complex ball and let $a$ and $b$ be two distinct points in its closure. Let $f$ be a real-analytic function on the complex unit sphere $\partial B^n.$ Suppose that for any complex line $L,$ meeting the…

We generalize the notion of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These conjugate functions are in general far from being…