Related papers: Normality criterion for logharmonic mapping

In this paper, we establish Lipschitz conditions for the norm of holomorphic mappings between the unit ball $\mathbb{B}^n$ in $\mathbb{C}^n$ and $X,$ a complex normed space. This extends the work of Djordjevi\'{c} and Pavlovi\'{c}.

This paper is focused on necessary conditions for hypoellipticity of an operator $L$ of the form $L=L_1(x)+g(x)L_2(y)$, where the operator $L_1$ is either elliptic or parabolic, $L_2$ is degenerately elliptic and $g(x)$ may itself vanish…

We estimate the norm of the harmonic Bergman projection in the context of harmonic Besov spaces. We obtain the two-side norm estimates in general Lp-case.

We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian…

In the present paper, we derive several conditions of linear combinations and convolutions of harmonic mappings to be univalent and convex in one direction, one of them gives a partial answer to an open problem proposed by Dorff. The…

A new approach to the solution of quasilinear nonelliptic first-order systems of inhomogeneous PDEs in many dimensions is presented. It is based on a version of the conditional symmetry and Riemann invariant methods. We discuss in detail…

This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is difference isomonodromic if and only if it is difference…

We show that on any Riemannian manifold with H\"older continuous metric tensor, there exists a $p$-harmonic coordinate system near any point. When $p = n$ this leads to a useful gauge condition for regularity results in conformal geometry.…

Let $h$ and $g$ be two analytic functions in the unit disc $\Delta$ that $g(0)=1$. Also let $\beta$ be a complex number with ${\rm Re}\{\beta\}>-1/2$. A function $f$ is said to be log--harmonic mapping if it has the following representation…

If $(M,g)$ is a compact Riemannian manifold of dimension $n\ge 2$ we give necessary and sufficient conditions for improved $L^p(M)$-norms of eigenfunctions for all $2<p\ne p_c=\tfrac{2(n+1)}{n-1}$, the critical exponent. Since improved…

The primary aim of this paper is to construct harmonic mapping associated with four parameter Wright functions. Further sufficient conditions have been established so that this harmonic mapping satisfies geometric properties such as…

The diamond and completely bounded norms for linear maps play an increasingly important role in quantum information science, providing fundamental stabilized distance measures for differences of quantum operations. Based on the theory of…

The harmonic inner radius $\sigma_H(\Omega)$ of a planar domain $\Omega$ is the largest constant with which a univalence criterion via the Schwarzian derivative holds for harmonic mappings. We show that…

Let G be a semisimple Lie group without compact factors, \Gamma be an irreducible lattice in G. In the first part of the article we give the necessary and sufficient condition under which a sequence of translates of probability…

In this note, we generalize biharmonic equation for rotationally symmetric maps ([4], [16], [10]) to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from…

For a paradigmatic case, the standard map, we discuss how the statistical description of the approach to equilibrium is related to the sensitivity to the initial conditions of the system. Using a numerical analysis we present an anomalous…

In this paper, we prove the boundary partial regularity for a class of coupled Dirac-harmonic maps satisfying a certain energy monotonicity inequality near the boundary.

In this paper we give a generalization of the normal holomorphic frames in the symplectic manifolds and find conditions for the integrability of complex structures.

We give necessary and sufficient conditions in terms of sign vectors for the injectivity of families of polynomial maps with arbitrary real exponents defined on the positive orthant. Our work relates and extends existing injectivity…

Let $\mathbf {x}_1,\ldots,\mathbf {x}_n$ be a random sample from a $p$-dimensional population distribution, where $p=p_n\to\infty$ and $\log p=o(n^{\beta})$ for some $0<\beta\leq1$, and let $L_n$ be the coherence of the sample correlation…