Related papers: Proper holomorphic maps between Reinhardt domains …
We consider mappings of domains of Riemannian manifolds that admit branch points and satisfy a certain condition regarding the distortion of the modulus of families of paths. We have established logarithmic estimates of distance distortion…
We prove a boundary version of the open mapping theorem for holomorphic maps between strongly pseudoconvex domains. That is, we prove that the local image of a holomorphic map $f:D\to D'$ close to a boundary regular contact point $p\in \de…
This expository paper is concerned with the properties of proper holomorphic mappings between domains in complex affine spaces. We discuss some of the main geometric methods of this theory, such as the Reflection Principle, the scaling…
We consider how the problem of determining normal forms for a specific class of nonholonomic systems leads to various interesting and concrete bridges between two apparently unrelated themes. Various ideas that traditionally pertain to the…
We prove a suite of results classifying holomorphic maps between configuration spaces of Riemann surfaces; we consider both the ordered and unordered setting as well as the cases of genus zero, one, and at least two. We give a complete…
We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains. It is shown that such mappings…
We establish a defect relation of holomorphic curves from a general open Riemann surface into a normal complex projective variety, with Zariski-dense image intersecting effective Cartier divisors.
In this note, we prove a rigidity result for proper holomorphic maps between unit balls that have many symmetries and which extend to $\mathcal{C}^2$-smooth maps on the boundary.
Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold…
The purpose of this note is two fold. First, we study the relation between a pair of H\'{e}non maps that share the same forward and backward non-escaping sets. Second, it is shown that there exists a continuum of $Short-\mathbb{C}^2$'s that…
We consider proper holomorphic maps of ball complements and differences in complex euclidean spaces of dimension at least two. Such maps are always rational, which naturally leads to a related problem of classifying rational maps taking…
In this article, we study holomorphic isometric embeddings between bounded symmetric domains. In particular, we show the total geodesy of any holomorphic isometric embedding between reducible bounded symmetric domains with the same rank.
In the case where both the domain and target manifolds are almost Hermitian, we introduce the concept of Hermitian pluriharmonic maps. We prove that any holomorphic or anti-holomorphic map between almost Hermitian manifolds is Hermitian…
We show how to express a conformal map of a general two connected domain in the plane such that neither boundary component is a point to a representative domain which has the virtue of having an explicit algebraic Bergman kernel function.…
We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…
In the paper the complex geodesics of a convex domain in $\mathbb C^n$ are studied. One of the main results of the paper provides certain necessary condition for a holomorphic map to be a complex geodesic for a convex domain in $\mathbb…
Given a bounded n-connected domain in the plane bounded by non-intersecting Jordan curves, and given one point on each boundary curve, L. Bieberbach proved that there exists a proper holomorphic mapping of the domain onto the unit disc that…
In this paper, we establish second main theorems for holomorphic maps with finite growth index on complex discs intersecting families of hypersurfaces (moving and fixed) in projective varieties, where the small term is detailed estimate for…
A characterization of $L_h^2$-domains of holomorphy in the class of Hartogs domains in $\Bbb C^2$ is given.
We give a complete description of bounded Reinhardt domains of finite boundary smoothness that have non-compact automorphism group. As part of this program, we show that the classification of domains with non-compact automorphism group and…