Related papers: Hyperbolic distances, nonvanishing holomorphic fun…

A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like…

The Schwarzian derivative provides a classical analytic measure of how far a holomorphic map of the disk is from being M\"obius, with Nehari's bounds giving sharp criteria for univalence. Independently, Thurston introduced a geometric…

Generalizing the slicing inequality for functions on convex bodies from [11], it was proved in [4] that there exists an absolute constant $c$ so that for any $n\in \mathbb N$, any $q\in [0,n-1)$ which is not an odd integer, any…

In this paper, we establish several results related to Crouzeix's conjecture. We show that the conjecture holds for contractions with eigenvalues that are sufficiently well-separated. This separation is measured by the so-called separation…

The purpose of the present paper is to prove existence of super-exponentially many compact orientable hyperbolic arithmetic $n$-manifolds that are geometric boundaries of compact orientable hyperbolic $(n+1)$-manifolds, for any $n \geq 2$,…

We show that if a 1-hyperbolic structurally finite entire function of type $(p,q)$, $p\ge 1$, is linearizable at an irrationally indifferent fixed point, then its multiplier satisfies the Brjuno condition. We also prove the generalized…

In 1984, Clunie and Sheil-Small proved that a sense-preserving harmonic function whose analytic part is convex, is univalent and close-to-convex. In this paper, certain cases are discussed under which the conclusion of this result can be…

We study the motion of a stochastic string in the background of a BTZ black hole. In the 1+1 dimensional boundary theory this corresponds to a very heavy external particle (e.g, a quark), interacting with the fields of a CFT at finite…

In this paper, we prove that there exist at least $[\frac{n+1}{2}]+1$ geometrically distinct brake orbits on every $C^2$ compact convex symmetric hypersurface $\Sg$ in $\R^{2n}$ for $n\ge 2$ satisfying the reversible condition $N\Sg=\Sg$…

Some of important univalence criteria for a non-constant meromorphic function $f(z)$ on the unit disk $\ID$ involve its pre-Schwarzian or Schwarzian derivative. We consider an appropriate norm for the pre-Schwarzian derivative, and discuss…

This paper makes two contributions towards determining some well-studied optimal constants in Fourier analysis \newa{of Boolean functions} and high-dimensional geometry. \begin{enumerate} \item It has been known since 1994 \cite{GL:94} that…

For 0 < c < 1/e the Julia set of f(z) = c exp(z) is an uncountable union of pairwise disjoint simple curves tending to infinity [Devaney and Krych 1984], the Hausdorff dimension of this set is two [McMullen 1987], but the set of curves…

Given a subset $\Lambda$ of $\mathbb Z_+:=\{0,1,2,\dots\}$, let $H^\infty(\Lambda)$ denote the space of bounded analytic functions $f$ on the unit disk whose coefficients $\widehat f(k)$ vanish for $k\notin\Lambda$. Assuming that either…

The first goal of this paper is to improve some of the results in \cite{BCPR}. Namely, we establish the $L_p$-Brunn-Minkwoski inequality for intrinsic volumes for origin-symmetric convex bodies that are close to the ball in the $C^2$ sense…

A number of classical results reflect the fact that if a holomorphic function maps the unit disk into itself taking the origin into the origin, and if some boundary point $b$ maps to the boundary, then the map is a magnification at $b$. We…

Let $D$ be a convex domain in the plane. Let $a_k$ be summable positive constants and let each $z_k$ lie in $D$. If the $z_k$ converge sufficiently rapidly to a boundary point of $D$ from within an appropriate Stolz angle then the function…

We prove sharp version of Riesz-Fej\'er inequality for functions in harmonic Hardy space $h^p(\mathbb{D})$ on the unit disk $\mathbb{D}$, for $p>1,$ thus extending the result from \cite{KPK} and resolving the posed conjecture.

The purpose of this paper is to develop the theory of holomorphic functions with modulus bounded by $1$ on the symmetrized skew bidisc \[ \mathbb{G}_{r} \stackrel{\rm def}{=} \Big\{( \lambda_{1}+r\lambda_{2} ,r\lambda_{1}\lambda_{2}):…

General estimates from below of holomorphic and subharmonic functions play one of the key roles in the theory of growth of holomorphic and subharmonic functions and in general in the theory of potential. At the same time, the most diverse…

In this paper, we prove the following result : let X be a complex manifold, hyperbolic for the Carath\'eodory distance and let U be an open set relatively compact in X. Then, there exists k<1 such that we get, for the Carath\'eodory…