Related papers: Holomorphic motions and complex geometry
We prove a generalisation of Rudin's theorem on proper holomorphic maps from the unit ball to the case of proper holomorphic maps from pseudoellipsoids.
We prove that a $C^{1,1}$-smooth bounded domain $D$ in $\C^n$ is linearly convex if and only if the convex hull of any two discs in $D$ with common center lies in $D.$
The classical integral representation formulas for holomorphic functions defined on pseudoconvex domains in Stein manifolds play an important role in the constructive theory of functions of several complex variables. In this paper we…
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…
We study the holomorphic embedding problem from a compact strongly pseudoconvex real algebraic hypersurface into a sphere of higher dimension. We construct a family of compact strongly pseudoconvex hypersurfaces $M_{\epsilon}$ in…
The aim of this paper is to prove that there exists no cohomogeneity one $G-$invariant proper biharmonic hypersurface into the Euclidean space ${\mathbb R}^n$, where $G$ denotes a tranformation group which acts on ${\mathbb R}^n$ by…
We present two geometric interpretations for complex multivectors and determinants: a little known one in terms of square roots of volumes, and a new one which uses fractions of volumes and allows graphical representations. The fraction…
Let $(\varphi_t)$, $(\phi_t)$ be two one-parameter semigroups of holomorphic self-maps of the unit disc $\mathbb D\subset \mathbb C$. Let $f:\mathbb D \to \mathbb D$ be a homeomorphism. We prove that, if $f \circ \phi_t=\varphi_t \circ f$…
This paper shows that every totally-geodesic isometry from the unit disk to a finite-dimensional Teichm\"uller space for the intrinsic Kobayashi metric is either holomorphic or anti-holomorphic; in particular, it is a Teichm\"uller disk.…
We extend a well-known result, about the unit ball, by H. Alexander to a class of balanced domains in $\mathbb{C}^n, \ n > 1$. Specifically: we prove that any proper holomorphic self-map of a certain type of balanced, finite-type domain in…
An existence theorem for stationary discs of strongly pseudoconvex domains in almost complex manifolds is proved. More precisely, it is shown that, for all points of a suitable neighborhood of the boundary and for any vector belonging to…
We construct examples illustrating that dynamically-defined distributions of holomorphic diffeomorphisms on compact complex manifolds are not necessarily holomorphic in any open subset. More precisely, for any $n\geq 5$, we construct a…
Given a domain of holomorphy $D$ in $\mathbb{C}^N$, $N\geq 2$, we show that the set of holomorphic functions in $D$ whose cluster sets along any finite length paths to the boundary of $D$ is maximal, is residual, densely lineable and…
We study the complexity of holomorphic isometries and proper maps from the complex unit ball to type IV classical domains. We investigate on degree estimates of holomorphic isometries and holomorphic maps with minimum target dimension. We…
We give an example of a pseudoconvex domain in a complex manifold whose $L^2$-Dolbeault cohomology is non-Hausdorff, yet the domain is Stein. The domain is a smoothly bounded Levi-flat domain in a two complex-dimensional compact complex…
We prove that a backward orbit with bounded Kobayashi step for a hyperbolic or strongly elliptic holomorphic self-map of a bounded strongly convex domain in the d-dimensional complex Euclidean space necessarily converges to a boundary fixed…
By considering a certain univalent function in the open unit disk U, that maps U onto a strip domain, we introduce a new class of analytic and close-to-convex functions by means of a certain non-homogeneous Cauchy-Euler-type differential…
We make a connection between the structure of the bidisc and a distinguished subgroup of its automorphism group. The automorphism group of the bidisc, as we know, is of dimension six and acts transitively. We observe that it contains a…
We define pointwise partial differential relations for holomorphic discs. Given a relative homotopy class, a relation, and a generic almost complex structure we provide the moduli space of discs which have an injective point with the…
A classical result in complex geometry says that the automorphism group of a manifold of general type is discrete. It is more generally true that there are only finitely many surjective morphisms between two fixed projective manifolds of…