Related papers: Deformations of Strongly Pseudoconvex Domains

Let $D=\{\rho<0\}$ be a smooth domain of finite type in an almost complex manifold (M,J) of real dimension four. We assume that the defining function $\rho$ is J-plurisubharmonic on a neighborhood of $\overline{D}$. We study the asymptotic…

We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between smooth strongly pseudoconvex domains in $\C^n$ are conformal with respect to the sub-Riemannian metric induced by the Levi form.…

We introduce the notion of extremal basis of tangent vector fields at a boundary point of finite type of a pseudo-convex domain in $\mathbb{C}^n$. Then we define the class of geometrically separated domains at a boundary point, and give a…

We propose a proof of the characterization of spherical hypersurfaces as the only strictly pseudoconvex hypersurfaces which have contracting germs of diffeomorphisms. Unlike previous proofs, our approach does not use Chern-Moser theory. It…

We show that the symmetrized bidisc may be exhausted by strongly linearly convex domains. It shows in particular the existence of a strongly linearly convex domain that cannot be exhausted by domains biholomorphic to convex ones.

We prove that if a holomorphic self-map $f\colon \Omega\to \Omega$ of a bounded strongly convex domain $\Omega\subset \mathbb C^q$ with smooth boundary is hyperbolic then it admits a natural semi-conjugacy with a hyperbolic automorphism of…

We introduce a class of volume-contracting surface diffeomorphisms whose dynamics is intermediate between one-dimensional dynamics and general surface dynamics. For that type of systems one can associate to the dynamics a reduced…

We show that in $\mathbb{C}^2$ if the set of strongly regular points are closed in the boundary of a smooth bounded pseudoconvex domain, then the domain is c-regular, that is, the plurisubharmonic upper envelopes of functions continuous up…

Let $D \subset \mathbb{C}^n$ be a smoothly bounded pseudoconvex Levi corank one domain with defining function $r$, i.e., the Levi form $\partial \bar {\partial} r$ of the boundary $\partial D$ has at least $(n - 2)$ positive eigenvalues…

Let N be a complete, simply-connected surface of constant curvature \kappa \leq 0. Moreover, suppose that \Omega and \tilde{\Omega} are strictly convex domains in N with the same area. We show that there exists an area-preserving…

We study real Campedelli surfaces up to real deformations and exhibit a number of such surfaces which are equivariantly diffeomorphic but not real deformation equivalent.

Following M.Abate and A.Saracco's work on strongly pseudoconvex domains in $\mathbb{C}^n$, we characterize Carleson measures of $A^2(D)$ in bounded convex domains with smooth boundary of finite type. We also give examples of Carleson…

We construct a class of bounded domains, on which the squeezing function is not uniformly bounded from below near a smooth and pseudoconvex boundary point.

We present a form of Schwarz's lemma for holomorphic maps between convex domains $D_1$ and $D_2$. This result provides a lower bound on the distance between the images of relatively compact subsets of $D_1$ and the boundary of $D_2$. This…

Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset…

We construct families of convex domains that are biholomorphic to bounded domains, but not bounded convex domains. This is accomplished by finding an obstruction related to the Gromov hyperbolicity of the Kobayashi metric.

We establish a weighted $L^p$ norm estimate for the Bergman projection for a class of pseudoconvex domains. We obtain an upper bound for the weighted $L^p$ norm when the domain is, for example, a bounded smooth strictly pseudoconvex domain,…

The Diederich-Forn{\ae}ss worm domain, an important example of a smoothly bounded pseudoconvex domain without a Stein neighborhood basis, provides key counterexamples in the theory of Several Complex Variables. In this paper, we examine its…

We prove that a strongly pseudoconvex domain with noncompact group of Kobayashi/Royden metric isometries must be biholomorphic to the unit ball.

We show that the graph of a holomorphic motion of the unit disc cannot be biholomorphic to a strongly pseudoconvex domain in C n .