Related papers: Canonical models on strongly convex domains via th…

We study general properties of holomorphic isometric embeddings of complex unit balls $\mathbb B^n$ into bounded symmetric domains of rank $\ge 2$. In the first part, we study holomorphic isometries from $(\mathbb B^n,kg_{\mathbb B^n})$ to…

We consider a convex solid cone $\mathcal{C}\subset\mathbb{R}^{n+1}$ with vertex at the origin and boundary $\partial\mathcal{C}$ smooth away from $0$. Our main result shows that a compact two-sided hypersurface $\Sigma$ immersed in…

In this article, we consider the ball model of an infinite dimensional complex hyperbolic space, i.e. the open unit ball of a complex Hilbert space centered at the origin equipped with the Caratheodory metric. We consider the group of…

In this article we continue the study of properties of squeezing functions and geometry of bounded domains. The limit of squeezing functions of a sequence of bounded domains is studied. We give comparisons of intrinsic positive forms and…

Looking to the fundamental domains of space groups we can investigate in which space they can be realized. If this space is hyperbolic, then the corresponding space group is also hyperbolic. In addition to the usual methods for…

We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…

In this article, we give a versal deformation for any transversely holomorphic foliation $\mathcal{F}_0$ given by the intersection of the orbits of a holomorphic vector field $\xi$ defined on a neighborhood of the closure of a bounded…

Many authors have studied the dynamics of hyperbolic transcendental entire functions; these are those for which the postsingular set is a compact subset of the Fatou set. Equivalenty, they are characterized as being expanding.…

We consider a complete, unbounded, hyperbolic metric space $X$ and a concave, nonzero and nondecreasing function $\omega:[0,+\infty)\to[0,+\infty)$ with $\omega(0)=0$ and study the space $\mathcal{C}_\omega(X)$ of uniformly continous…

Let $(M, \partial M)$ be a compact 3-manifold with boundary, which admits a convex co-compact hyperbolic metric. We consider the hyperbolic metrics on $M$ such that the boundary is smooth and strictly convex. We show that the induced…

Given a hyperbolic domain, the nearest point retraction is a conformally natural homotopy equivalence from the domain to the boundary of the convex core of its complement. Marden and Markovic showed that if the domain is uniformly perfect,…

For $\alpha > -1$ and $\beta >0, $ let $\mathcal{B}_{\mathcal{H}}^0(\alpha, \beta)$ denote the class of sense preserving harmonic mappings $f=h+\overline{g}$ in the open unit disk $\mathbb{D}$ satisfying $|zh''(z)+\alpha(h'(z)-1)|\leq…

We investigate the dynamical behaviour of a holomorphic map on a $f-$invariant subset $\mathcal{C}$ of $U,$ where $f:U \to \mathbb{C}^k.$ We study two cases: when $U$ is an open, connected and polynomially convex subset of $\mathbb{C}^k$…

In this paper, we provide a class of domains in $\mathbb{C}^3$, such that every holomorphic self-map of that domain either has a fixed point or the sequence of iterates is compactly divergent. In particular, it follows that the symmetrized…

We study the boundaries of non-univalent simply connected Baker domains of transcendental maps (both entire and meromorphic), of hyperbolic and simply parabolic type. We prove non-ergodicity and non-recurrence for the boundary map, and…

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

We study the dynamics of polynomial maps on the boundary of the central hyperbolic component $\mathcal H_d$. We prove the local connectivity of Julia sets and a rigidity theorem for maps on the regular part of $\partial\mathcal H_d$. Our…

Chaotic hyperbolic dynamical systems enjoy a surprising degree of rigidity, a fact which is well known in the mathematics community but perhaps less so in theoretical physics circles. Low-dimensional hyperbolic systems are either conjugate…

In this paper, we study the domains in $\mathbb{C}^n$ that are invariant under the positive flows of some globally defined, complete holomorphic vector field with a globally attracting fixed point at the origin. Our first result says that…

In a previous work on the large $|k|$ behavior of complex geometric optics solutions to a system of d-bar equations, we treated in detail the situation when a certain potential is the characteristic function of a strictly convex set with…