Related papers: A Wong-Rosay type theorem for proper holomorphic s…

We construct a complete proper holomorphic embedding from any strictly pseudoconvex domain with $\mathcal{C}^2$-boundary in $\mathbb{C}^n$ into the unit ball of $\mathbb{C}^N$, for $N$ large enough, thereby answering a question of Alarcon…

We investigate subgroups of SL (n,Z) which preserve an open nondegenerate convex cone in real n-space and admit in that cone as fundamental domain a polyhedral cone of which some faces are allowed to lie on the boundary. Examples are…

We introduce a new notion, called quasi-holomorphic maps. These are real smooth maps equipped with a structure that imitates the singularities and singularity stratifications of holomorphic maps on the source and target manifolds, although…

In this paper, we prove that the closure of a bounded pseudoconvex domain, which is spirallike with respect to a globally asymptotic stable holomorphic vector field, is polynomially convex. We also provide a necessary and sufficient…

A map from a manifold to a Euclidean space is said to be k-regular if the image of any distinct k points are linearly independent. In this paper, we give some lower bounds of the dimension of the ambient Euclidean space for complex…

In this article we prove that, for an oriented PL $n$-manifold $M$ with $m$ boundary components and $d_0\in \mathbb N$, there exist mutually disjoint closed Euclidean balls and a $\mathsf K$-quasiregular mapping $M \to \mathbb S^n \setminus…

We give a counterexample to the following conjecture: the set of isolated periodic points of an automorphism of degree at least two on an affine space is a set of bounded height. As a positive result, we prove that any cohomologically…

Let D be a domain in C^n with smooth boundary, of finite 1-type at a point p in the boundary and such that the closure of D has a basis of Stein Runge neighborhoods. Assume that there exists an analytic disc which intersects the closure of…

In this paper, we provide a class of domains in $\mathbb{C}^3$, such that every holomorphic self-map of that domain either has a fixed point or the sequence of iterates is compactly divergent. In particular, it follows that the symmetrized…

We consider holomorphic maps $f: U \to U$ for a hyperbolic domain $U$ in the complex plane, such that the iterates of $f$ converge to a boundary point $\zeta$ of $U$. By a previous result of the authors, for such maps there exist nice…

The purpose of this article is towards systematically characterizing (holomorphic) retracts of domains of holomorphy; to begin with, bounded balanced pseudoconvex domains $B \subset \mathbb{C}^N$. Specifically, we show that every retract of…

We study proper holomorphic maps of annuli in complex Euclidean spaces, that is, domains with $U(n)$ as the automorphism group. By the Hartogs phenomenon and a result of Forstneri\v{c}, such maps are always rational and extend to proper…

In this note, we prove, for instance, that the automorphism group of a rational manifold X which is obtained from CP^k by a finite sequence of blow-ups along smooth centers of dimension at most r with k>2r+2 has finite image in…

We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the…

We study toplogical properties of attracting sets for automorphisms of $\mathbb{C}^k$. Our main result is that a generic volume preserving automorphism has a hyperbolic fixed point with a dense stable manifold. We prove the same result for…

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…

We establish rigidity (or uniqueness) theorems for nc automorphisms which are natural extensions of clasical results of H.~Cartan and are improvements of recent results. We apply our results to nc-domains consisting of unit balls of…

We prove that every bounded smooth domain of finite d'Angelo type in $\mathbb{C}^2$ endowed with the Kobayashi distance is Gromov hyperbolic and its Gromov boundary is canonically homeomorphic to the Euclidean boundary. We also show that…

In this article we prove a global result in the spirit of Basener's theorem regarding the relation between q-pseudoconvexity and q-holomorphic convexity: we prove that any smoothly bounded strictly q-pseudoconvex open subset of the complex…

In this paper, we explore the local geometry of dynamical systems $\dot{x}=F(x)$ with real time parameterization, where $F$ is holomorphic on connected open subsets of $\mathbb{C}\stackrel{\sim}{=}\mathbb{R}^2$. We describe the geometry of…