Related papers: Fatou-Bieberbach domains in $\mathbb C^n\setminus\…

K be a field and let m and n be positive integers, where m does not exceed n. We say that a non-zero subspace of m x n matrices over K is a constant rank r subspace if each non-zero element of the subspace has rank r, where r is a positive…

We consider the analogue for regular maps from affine varieties to suitable algebraic manifolds of Oka theory for holomorphic maps from Stein spaces to suitable complex manifolds. The goal is to understand when the obstructions to…

Let $\Omega$ be a pseudoconvex domain in $\mathbb C^n$ with smooth boundary $b\Omega$. We define general estimates $(f\text{-}\mathcal M)^k_{\Omega}$ and $(f\text{-}\mathcal M)^k_{b\Omega}$ on $k$-forms for the complex Laplacian $\Box$ on…

In this paper, we show that any convex affine domain with a nonempty limit sets on the boundary under the action of the identity component of the automorphism group cannot cover a compact affine manifold with a parallel volume, which is a…

We show that any compact subset of $\R^d$ which is the closure of a bounded star-shaped Lipschitz domain $\Omega$, such that $\complement \Omega$ has positive reach in the sense of Federer, admits an \emph{optimal AM} (admissible mesh),…

This paper works on the structure of infinitely connected Fatou damains of rational maps in terms of Koebe uniformization. Due to the complicated boundary behavior, the existing uniformization results are failed to apply in general. We…

This paper treats a holomorphic self-mapping f: Omega --> Omega of a bounded domain Omega in a separable Hilbert space H with a fixed point p. In case the domain is convex, we prove an infinite-dimensional version of the…

In this short note we consider very general bounded minimal homogeneous domains. Under certain natural additional conditions new sharp results on Bergman type analytic spaces in minimal bounded homogeneous domains are obtained. Domains we…

Kobayashi [Duke Math. J. (1992)] gave a necessary condition for the existence of compact Clifford-Klein forms in terms of Cartan projections and non-compact dimensions of reductive subgroups. We extend his method to non-reductive subgroups,…

The boundary of every relatively compact Stein domain in a complex manifold of dimension at least two is connected. No assumptions on the boundary regularity are necessary. The same proofs hold also for $q$-complete domains, and in the…

Let $C_b^{k,\omega}(\mathbb R^n)$ be the Banach space of $C^k$ functions on $\mathbb R^n$ bounded together with all derivatives of order $\le k$ and with derivatives of order $k$ having moduli of continuity majorated by $c\cdot\omega$,…

We show geodesic completeness of certain compact locally symmetric pseudo-Riemannian manifolds of signature $(2,n)$. Our model space $\mathbf{X}$ is a $1$-connected, indecomposable symmetric space of signature $(2,n)$, that admits a unique…

Let K be an arbitrary (commutative) field with at least three elements, and let n, p and r be positive integers with r<=min(n,p). In a recent work, we have proved that an affine subspace of M_{n,p}(K) containing only matrices of rank…

We consider a definably complete locally o-minimal expansion of an ordered field. We treat two topics in this paper. The first topic is a definable $\mathcal C^r$ approximation of a definable $\mathcal C^{r-1}$ map between definable…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^2$ with Lipschitz boundary or a bounded convex domain in $\mathbb{C}^n$ and $\phi\in C(\overline{\Omega})$ such that $H_{\phi}$ is compact on $A^2(\Omega)$. Then $\phi\circ f$ is…

We show that for bounded domains in $\mathbb C^n$ with $\mathcal C^{1,1}$ smooth boundary, if there is a closed set $F$ of $2n-1$-Lebesgue measure $0$ such that $\partial \Omega \setminus F$ is $\mathcal C^{2}$-smooth and locally…

We introduce a continuous domain for function spaces over topological spaces which are not core-compact. Notable examples of such topological spaces include the real line with the upper limit topology, which is used in solution of initial…

In this paper, we characterize weakly pseudoconvex domains of finite type in $\mathbb C^n$ in terms of the boundary behavior of automorphism orbits by using the scaling method.

In this article we construct many examples of properly convex irreducible domains divided by Zariski dense relatively hyperbolic groups in every dimension at least 3. This answers a question of Benoist. Relative hyperbolicity and non-strict…

A new proof of Oka's lemma is given for smoothly bounded, pseudoconvex domains $D\subset\mathbb{C}^n$. The method of proof is then also applied to other convexity-like hypotheses on the boundary of $D$.