Related papers: Perturbation of domains and automorphism groups

We prove a topological stability result for the actions of hyperbolic groups on their Bowditch boundaries. More precisely, we show that a sufficiently small perturbation of the standard boundary action, if assumed on each parabolic subgroup…

The set of badly approximable $m \times n $ matrices is known to have Hausdorff dimension $mn $. Each such matrix comes with its own approximation constant $c$, and one can ask for the dimension of the set of badly approximable matrices…

Hahn groups endowed with the canonical valuation play a fundamental role in the classification of valued abelian groups. In this paper we study the group of valuation (respectively order) preserving automorphisms of a Hahn group $G$. Under…

We consider a problem whether a given Lie group can be realized as the group of all biholomorphic automorphisms of a bounded domain in the affine complex space. In an earlier paper of 1990, we proved the result for connected linear Lie…

One of our main goals in this paper is to understand the behavior of limit sets of a diverging sequence of Schottky groups in the group of isometries of the N-dimensional hyperbolic space. This leads us to a generalization of a classical…

We investigate how the integrability of the derivatives of Orlicz-Sobolev mappings defined on open subsets of $\mathbb{R}^n$ affect the sizes of the images of sets of Hausdorff dimension less than $n$. We measure the sizes of the image sets…

We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore, the gap-filling spectra contribute to quantised current…

We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. We show, with some examples, that representation theory of semigroups is related to usual constructions in…

In this work we consider the asymptotic behavior of the nonlinear semigroup defined by a semilinear parabolic problem with homogeneous Neumann boundary conditions posed in a bounded region of the plane that degenerates into a line segment…

We show that each pseudoconvex domain $\Omega\subset {\mathbb C}^n$ admits a holomorphic map $F$ to ${\mathbb C}^m$ with $|F|\le C_1 e^{C_2 \hat{\delta}^{-6}}$, where $\hat{\delta}$ is the minimum of the boundary distance and…

In this paper we study domains in flag manifolds which are bounded in an affine chart and whose projective automorphism group acts co-compactly. In contrast to the many examples in real projective space, we will show that no examples exist…

In this paper, we study the Hausdorff dimension of the Floyd and Bowditch boundaries of a relatively hyperbolic group, and show that for the Floyd metric and shortcut metrics respectively, they are are both equal to a constant times the…

We prove that every 2-local automorphism of the unitary group or the general linear group on a complex infinite-dimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their…

We study holomorphic isometries between bounded symmetric domains with respect to the Bergman metrics up to a normalizing constant. In particular, we first consider a holomorphic isometry from the complex unit ball into an irreducible…

In this paper we give some quantative characteristics of boundary asymptotic behavior of semigroups of holomorphic self-mappings of the unit disk including the limit curvature of their trajectories at the boundary Denjoy--Wolff point. This…

Let $1 \to N \to G \to H \to 1$ be an abelian extension. The purpose of this paper is to study the problem of extending automorphisms of $N$ and lifting automorphisms of $H$ to certain automorphisms of $G$.

Using McMullen's Hausdorff dimension algorithm, we study numerically the dimension of the limit set of groups generated by reflections along three geodesics on the hyperbolic plane. Varying these geodesics, we found four minima in the…

We consider a family of chaotic Bose-Hubbard Hamiltonians (BHH) parameterized by the coupling strength $k$ between neighboring sites. As $k$ increases the eigenstates undergo changes, reflected in the structure of the Local Density of…

In the present paper, a series of results and examples that explore the structural features of H-commutative semigroups are provided. We also generalise a result of Isbell from commutative semigroups to H-commutative semigroups by showing…

Let F be a local field of positive characteristic, and let G be either a Heisenberg group over F, or a certain (nonabelian) two-dimensional unipotent group over F. If H is an arithmetic subgroup of G, we provide an explicit description of…