Related papers: Caratheodory convergence and harmonic measure

We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two…

This paper gives a definition of g-harmonic functions and shows the relation between the g-harmonic functions and g-martingales. It's direct to construct such relation under smooth case, but for continuous case we need the theory of…

In this paper we characterize sums of CR functions from competing CR structures in two scenarios. In one scenario the structures are conjugate and we are adding to the theory of pluriharmonic boundary values. In the second scenario the…

We study convergence almost everywhere of sequences of Schr\"odinger means. We also replace sequences by uncountable sets.

This paper aims to review the measure synchronization, a weak form of synchronization observed in coupled Hamiltonian systems, briefly. This synchronization is characterized by a Hamiltonian system that displays either quasiperiodic or…

We give improved bounds for the distortion of the Hausdorff dimension under quasisymmetric maps in terms of the dilatation of their quasiconformal extension. The sharpness of the estimates remains an open question and is shown to be closely…

Let $D \subset \mathbb{C}$ be a domain with $0 \in D$. For $R>0$, let ${{\hat \omega }_D}\left( {R} \right)$ denote the harmonic measure of $ D \cap \left\{ {\left| z \right| = R} \right\}$ at $0$ with respect to the domain $ D \cap \left\{…

Asymptotic $L_p$-convergence, which resembles convergence in $L_p$, was introduced to address a question in diffusive relaxation. This note aims to compare asymptotic $L_p$-convergence with convergence in measure and in weak $L_p$ spaces.…

We define a new condition number adapted to directionally uniform perturbations. The definitions and theorems can be applied to a large class of problems. We show the relation with the classical condition number, and study some interesting…

We give a short proof of the convergence to the boundary of Riemann maps on varying domains. Our proof provides a uniform approach to several ad-hoc constructions that have recently appeared in the literature.

We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.

Entanglement characteristics of a pair coherent state is studied using entanglement of superposition. It is demonstrated only few states in the expansion of a pair coherent state, in a harmonic oscillator basis, contribute significantly to…

We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and…

Harmonicity of holomorphic maps between various subclasses of almost contact metric manifolds is discussed. Consequently, some new results are obtained. Also some known results are recovered, some of them are generalized and some of them…

We estimate the growth of the canonical integral of Hadamard-Weierstrass of measure of finite order on the complex plane by the type of counting function or average counting function of this measure

In this short note we consider very general bounded minimal homogeneous domains. Under certain natural additional conditions new sharp results on Bergman type analytic spaces in minimal bounded homogeneous domains are obtained. Domains we…

Recently, Benini et al. showed that, in simply connected wandering domains of entire functions, all pairs of orbits behave in the same way relative to the hyperbolic metric, thus giving us our first insight into the general internal…

We introduce and study the notion of plurisubharmonic functions in calibrated geometry. These functions generalize the classical plurisubharmonic functions from complex geometry and enjoy their important properties. Moreover, they exist in…

First, we give the definition for quasi-nearly subharmonic functions, now for general, not necessarily nonnegative functions, unlike previously. We point out that our function class incudes, among others, quasisubharmonic functions, nearly…

We develop classical balayage (sweeping) measures and subharmonic functions on the ray system $S$ with a general origin on the complex plane $\mathbb C$. This allows for a subharmonic function $v$ on $\mathbb C$ to construct also a…