Related papers: A weak notion of strict pseudo-convexity. Applicat…

There exist several interesting results in the literature on subnormal operator tuples having their spectral properties tied to the geometry of strictly pseudoconvex domains or to that of bounded symmetric domains in $\C^n$. We introduce a…

The central purpose of the present paper is to study boundary behavior of squeezing functions on bounded domains. We prove that the squeezing function of a strongly pseudoconvex domain tends to 1 near the boundary. In fact, such an estimate…

Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity \delta_\Omega of a set \Omega. We also show that \lim_{\epsilon \to 0}…

The class of convex sets that admit approximations as Minkowski sum of a compact convex set and a closed convex cone in the Hausdorff distance is introduced. These sets are called approximately Motzkin-decomposable and generalize the notion…

Let $\Omega\subset \mathbb{C}^n$ be a smooth bounded pseudoconvex domain and $A^2 (\Omega)$ denote its Bergman space. Let $P:L^2(\Omega)\longrightarrow A^2(\Omega)$ be the Bergman projection. For a measurable $\varphi:\Omega\longrightarrow…

We show that a smooth bounded domain in $\mathbb{C}^n$ admitting partial pseudoconvex exhaustion remains partial pseudoconvex. The main ingredient of the proof is based on a new characterization of hyper-$q$-convex domains. Furthermore, we…

We study the boundary behaviour of the Fefferman--Szeg\"o metric and several associated invariants in a $C^\infty$-smoothly bounded strictly pseudoconvex domain.

We provide a novel approach to approximate bounded Lipschitz domains via a sequence of smooth, bounded domains. The flexibility of our method allows either inner or outer approximations of Lipschitz domains which also possess weakly defined…

For any pseudoconvex Runge domain $\Omega\subset\mathbb{C}^2$ we prove that every closed discrete subset in $\Omega$ is contained in a properly embedded complex curve in $\Omega$ with any prescribed topology (possibly infinite).

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 prove that for every $n \ge 2$, there exists a pseudoconvex domain $\Omega \subset \mathbb{C}^n$ such that $\mathfrak{c}^0(\Omega) \subsetneq \mathfrak{c}^1(\Omega)$, where $\mathfrak{c}^k(\Omega)$ denotes the core of $\Omega$ with…

A flag domain of a real from $G_0$ of a complex semismiple Lie group $G$ is an open $G_0$-orbit $D$ in a (compact) $G$-flag manifold. In the usual way one reduces to the case where $G_0$ is simple. It is known that if $D$ possesses…

This paper aims to give a further study on quasi-convex subsets in Alexandrov spaces with lower curvature bound which are introduced in [SSW]. We first provide new insights on quasi-convex subsets (Theorem A and Corollary C), and then as…

We construct a bounded domain $\Omega$ in $\mathbb{C}^2$ with boundary of class $\mathcal{C}^{1,1}$, such that $\overline{\Omega}$ has a Stein neighborhood basis, but is not $s$-H-convex for any real number $s\geq{1}$.

This paper is devoted to a systematic study and characterizations of the fundamental notions of variational and strong variational convexity for lower semicontinuous functions. While these notions have been quite recently introduced by…

This paper deals with some geometrical properties of solutions of some semilinear elliptic equations in bounded convex domains or convex rings. Constant boundary conditions are imposed on the single component of the boundary when the domain…

We prove that, if $\Omega\subset \mathbb{R}^n$ is an open bounded starshaped domain of class $C^2$, the constancy over $\partial \Omega$ of the function $$\varphi(y) = \int_0^{\lambda(y)} \prod_{j=1}^{n-1}[1-t \kappa_j(y)]\, dt$$ implies…

Let $\Omega \subset \mathbb{R}^{n+1}$, $n \geq 1$, be an open and connected set. Set $\mathcal{T}_n$ to be the set of points $\xi \in \partial \Omega$ so that there exists an approximate tangent $n$-plane for $\partial\Omega$ at $\xi$ and…

For a domain $D$ of $\mathbb{C}^n$ which is weakly $q$-pseudoconvex or $q$-pseudoconcave we give a sufficient condition for subelliptic estimates for the $\bar{\partial}$-Neumann problem. The paper extends to domains which are not…

In this article, we investigate the (big) Hankel operators $H_f$ on Hardy spaces of strongly pseudoconvex domains with smooth boundaries in $\mathbb{C}^n$. We also give a necessary and sufficient condition for boundedness of the Hankel…