Related papers: Harmonic functions with highly intersecting zero s…

The main aim of this paper is to study existence and stability properties of rotationally symmetric proper biharmonic maps between two $m$-dimensional models (in the sense of Greene and Wu). We obtain a complete classification of…

We examine the maximal domain of radial harmonic functions on harmonic spaces in the context of positive, zero, and negative curvature.

In most classical holomorphic function spaces on the unit disk in which the polynomials are dense, a function $f$ can be approximated in norm by its dilates $f_r(z):=f(rz)~(r<1)$, in other words, $\lim_{r\to1^-}\|f_r-f\|=0$. We construct a…

We provide sharp upper bounds for the number of symmetrizations required to transform a star shaped set in ${\mathbb R}^n$ arbitrarily close (in the Hausdorff metric) to the Euclidean ball.

Many authors have examined various boundary behaviors of injective harmonic mappings in the open unit disk. Building on Laugesen's work, Bshouty and others explored the boundary behavior of harmonic mappings under different conditions. In…

For systems of equations with an infinite set of roots, one can sometimes obtain Kushnirenko-Bernstein-Khovanskii type theorem if replace the number of roots by their asymptotic density. We consider systems of entire functions with…

Associated to a holomorphic quadratic differential is a unit ball of the measured lamination space. The Thurston volume of the unit ball defines a function on the moduli space. We show that the volume function is not proper and characterize…

We consider the convolution of half-plane harmonic mappings with respective dilatations $(z+a)/(1+az)$ and $e^{i\theta}z^{n}$, where $-1<a<1$ and $\theta\in\mathbb{R},n\in\mathbb{N}$. We prove that such convolutions are locally univalent…

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…

Let $E = L_p, \; 1<p\leq 2,$ and $A : E \to E^*$ be a bounded monotone map such that $0 \in R(A)$. In this paper, we introduce and study an algorithm for approximating zeros of $A$. Furthermore, we study the application of this algorithm to…

We present some results about harmonic maps with possibly infinite energy from punctured Riemann surfaces to CAT(0) spaces. In particular, we give precise estimates of their energy growth near the punctures and prove their uniqueness.

Bounded holomorphic interpolation problems associated to finitely many data have, in general, distinct solutions. Uniqueness arises only in some convex extreme configurations. Rational inner functions in a polydisk are the best understood…

We consider several ways to test for topology directly in harmonic space by comparing the measured a_lm with the expected correlation matrices. Two tests are of a frequentist nature while we compute the Bayesian evidence as the third test.…

A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in the study of nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a…

We study the problem of placing effective upper bounds for the number of zeros of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound, polynomially growing on the frontier of…

For minimizers in a geometrically nonlinear Cosserat model for micropolar elasticity of continua, we prove interior H\"older regularity, up to isolated singular points that may be possible if the exponent $p$ from the model is $2$ or in…

Let \(\mathbb D\) denote the unit disc in \(\mathbb C\). For a domain \(D\subset\mathbb C\) and a point \(p\in D\), let \(M_D(p)\) denote the supremum of \(\|df_0\|\) over all harmonic maps \(f:\mathbb D\to D\) with \(f(0)=p\) whose…

We prove that the existence of infinitely many $(m_k, n_k) \in \mathbb{N}^2$ such that the difference of harmonic numbers $H_{m_k} - H_{n_k}$ approximates 1 well $$ \lim_{k \rightarrow \infty} \left| \sum_{\ell = n}^{m_k} \frac{1}{\ell} - 1…

Inspired by the work of Karamata, we consider an extremization problem associated with the probability of intersecting two random chords inside a circle of radius $r, \, r \in (0,1]$, where the endpoints of the chords are drawn according to…

In this note, we study the Dirichlet problem for harmonic maps from strongly rectifiable spaces into regular balls in $\CAT(1)$ space. Under the setting, we prove that the Korevaar-Schoen energy admits a unique minimizer.