Related papers: Model pseudoconvex domains and bumping
Let $1\leq q\leq (n-1)$. We first show that a necessary condition for a Hankel operator on $(0,q-1)$-forms on a convex domain to be compact is that its symbol is holomorphic along $q$-dimensional analytic varieties in the boundary. Because…
Homogeneous complex manifolds satisfying various types of Levi conditions are considered. Classical results which were of particular interest to Andreotti are recalled. Convexity and concavity properties of flag domains are discussed in…
We give a description (direct formulas) of all complex geodesics in a convex tube domain in $\CC^n$ containing no complex affine lines, expressed in terms of geometric properties of the domain. We next apply that result to give formulas (a…
We prove that an open set $\Omega \subset \mathbb{R}^n$ can be approximated by smooth sets of uniformly bounded perimeter from the interior if and only if the open set $\Omega$ satisfies \begin{align*} &\qquad…
The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…
In this paper we study the global geometry of the Kobayashi metric on "convex" sets. We provide new examples of non-Gromov hyperbolic domains in $\mathbb{C}^n$ of many kinds: pseudoconvex and non-pseudocon \newline -vex, bounded and…
In this note we construct smooth bounded domains $\Omega \subset \mathbb R^2$, other than disks, for which the overdetermined problem $$ \left\{ \begin{alignedat}{2} \Delta u + \lambda u &= 0 &\qquad& \text{ in } \Omega, \newline u &= b…
We study the semicontinuity of automorphism groups for perturbations of domains in complex space or in complex manifolds. We provide a new approach to the study of such results for domains having minimal boundary smoothness. The emphasis in…
We give a necessary and sufficient condition for gluings of hyperconvex metric spaces along weakly externally hyperconvex subsets in order that the resulting space be hyperconvex. This leads to a full characterization of gluings of two…
We construct a strictly pseudoconvex domain with smooth boundary whose squeezing function is not plurisubharmonic.
We prove some refined asymptotic estimates for postive blowing up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$; $\Omega$ being a smooth bounded domain of $\rn$, $n\geq 3$.…
In this paper we deal with the following question: is it true that any bounded smooth pseudoconvex domain in $\mathbb{C}^n$ whose boundary contains a $q$-dimensional complex manifold $M$ necessarily has a noncompact…
The purpose of this paper is to prove that if a pseudoconvex domains $\Omega\subset\mathbb{C}^n$ satisfies Bell-Ligocka's Condition R and admits a ``good" dilation, then the Bergman projection has local $L^p$-Sobolev and H\"older estimates.…
After a study of the Kobayashi metrics on certain scaled domains, we show the stabilities of the infinitesimal Kobayashi metrics and the integrated distances in different scaling processes. As an application, we prove that bounded…
Given an open bounded subset $\Omega$ of $\mathbb{R}^n$, which is convex and satisfies an interior sphere condition, we consider the pde $-\Delta_{\infty} u = 1$ in $\Omega$, subject to the homogeneous boundary condition $u = 0$ on…
In the paper we study the geometry of semitube domains in $\mathbb C^2$. In particular, we extend the result of Burgu\'es and Dwilewicz for semitube domains dropping out the smoothness assumption. We also prove various properties of…
On a bounded strictly pseudoconvex domain in $\mathbb{C}^n$, $n>1$, the smoothness of the Cheng-Yau solution to Fefferman's complex Monge-Ampere equation up to the boundary is obstructed by a local curvature invariant of the boundary. For…
While intersections of convex sets are convex, their unions have rather complicated behavior. Some natural contexts where they appear include duality arguments involving boundaries of convex sets and valuations, which have an Euler…
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…
Let $D$ be a bounded domain in $\mathbf C^2$ with a non-compact group of holomorphic automorphisms. Model domains for $D$ are obtained under the hypothesis that at least one orbit accumulates at a boundary point near which the boundary is…