Related papers: Strong Stein neighborhood bases
For a domain $D \subset \mathbb C^n$, the relationship between the squeezing function and the Fridman invariants is clarified. Furthermore, localization properties of these functions are obtained. As applications, some known results…
Some invariant sets may attract a nearby set of initial conditions but nonetheless repel a complementary nearby set of initial conditions. For a given invariant set $X\subset\R^n$ with a basin of attraction $N$, we define a stability index…
A Daniell-Stone type characterization theorem for Aumann integrals of set-valued measurable functions will be proven. It is assumed that the values of these functions are closed convex upper sets, a structure that has been used in some…
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 $D$.
We show that invariant submanifolds with boundary, and more generally with corners which are normally expanded by an endomorphism are persistent as $a$-regular stratifications. This result will be shown in class $C^s$, for $s\ge 1$. We…
We consider the situation of a dominant meromorphic self-map $f: X -rightarrow X$, where $X$ is a compact K\"ahler manifold of dimension $n > 1$. Suppose there is an embedded copy of $\mathbb{P}^1$ that is invariant under $f$, with $f$…
We prove that every reduced Stein space admits a holomorphic function without critical points. Furthermore, any closed discrete subset of such a space is the critical locus of a holomorphic function. We also show that for every complex…
We apply the methods developed in [Br1] to study holomorphic functions of slow growth on coverings of pseudoconvex domains in Stein manifolds. In particular, we extend and strengthen certain results of Gromov, Henkin and Shubin [GHS] on…
Under a plausible geometric hypothesis, we show that a biholomorphic mapping of smoothly bounded, pseudoconvex domains extends to a diffeomorphism of the closures.
Let $\Omega$ be a domain in $\mathbb C^n$. Suppose that $\partial\Omega$ is smooth pseudoconvex of D'Angelo finite type near a boundary point $\xi_0\in \partial\Omega$ and the Levi form has corank at most $1$ at $\xi_0$. Our goal is to show…
The purpose of this article is twofold. First, we prove that the squeezing function approaches 1 near strongly pseudoconvex boundary points of bounded domains in $\mathbb{C}^{n+1}$. Second, we show that the squeezing function approaches 1…
We investigate structural properties of the cone of roots of relative Steiner polynomials of convex bodies. We prove that they are closed, monotonous with respect to the dimension, and that they cover the whole upper half-plane, except the…
In this note, we discuss the following problem: Given a smoothly bounded strongly pseudoconvex domain $D$ in $\mathbb{C}^n$, can we guarantee the existence of geodesics for the Kobayashi--Fuks metric which ``spiral around" in the interior…
We study the existence of topologically closed complex curves normalized by bordered Riemann surfaces in complex spaces. Our main result is that such curves abound in any noncompact complex space admitting an exhaustion function whose Levi…
Motivated by applications in materials science, a set of quasiconvexity at the boundary conditions is introduced for domains that are locally diffeomorphic to cones. These conditions are shown to be necessary for strong local minimisers in…
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…
The Levi geometry at weakly pseudoconvex boundary points of domains in C^n, n \geq 3, is sufficiently complicated that there are no universal model domains with which to compare a general domain. Good models may be constructed by bumping…
We give an example of a bounded Stein domain in $\mathbb{C}^n$, with smooth boundary, which is not Runge and whose intersection with every complex line is simply connected.
The main result is that, for any projective compact analytic subset A of dimension q>0 in a reduced complex space X, there is a neighborhood U of A such that, for any covering space Z of X in which the lifting B of A has no noncompact…
The disc property is formulated for domains in $\mathbb{C}^n$. Holomorphic Lipschitz functions enjoy a gain in the order of Lipschitz regularity along the complex tangential direction on domains with disc property. Disc property is studied…