Related papers: Landau type theorem for $\alpha$-harmonic mappings
We prove a Schwarz type lemma for harmonic mappings between the unit and a geodesic line in a Riemenn surface.
In this paper, we will use the normalized intetral Ricci curvature to investigate Liouville type property of $ p $ harmonic function on Riemannian manifold. secondly, we will use the BiRic curvature to obtian Liuville theorem for $ p $…
In this paper, we obtained Liouville theorem for $ \phi $-$F$-symphonic map , $ \phi $-$F$-harmonic map and $ \phi $-$\Phi_{S, p, \varepsilon}$ harmonic map with free boundary on metric measure space.
In this paper, the Schwarz type and Schwarz-Pick type inequalities for solutions of $\alpha$-harmonic equation for $\alpha>-1$ are investigated. By making use of the integral of trigonometric functions, we obtain the two types of…
The aim of this paper is to establish properties of the solutions to the $\alpha$-harmonic equations: $\Delta_{\alpha}(f(z))=\partial{z}[(1-{|{z}|}^{2})^{-\alpha} \overline{\partial}{z}f](z)=g(z)$, where…
In this paper, we investigate some properties on harmonic functions and solutions to Poisson equations. First, we will discuss the Lipschitz type spaces on harmonic functions. Secondly, we establish the Schwarz-Pick lemma for harmonic…
In this paper, we first establish the Schwarz-Pick lemma of higher-order and apply it to obtain a univalency criteria for planar harmonic mappings. Then we discuss distortion theorems, Lipschitz continuity and univalency of planar harmonic…
We prove a version of Smirnov type theorem and Charatheodory type theorem for a harmonic homeomorphism of the unit disk onto a Jordan surface with rectifiable boundary. Further we establish the classical isoperimetric inequality and…
In a recent paper the first and the third authors introduced the notion of horizontal \alpha-harmonic map, with respect to a given C^1 planes distribution P_T on all R^m. The goal of this paper is to investigate compactness and quantization…
We study a second order differential equation corresponding to rotationally symmetric $F$-harmonic maps between certain noncompact manifolds. We show unique continuation and Liouville's type theorems for positive solutions. Asymptotic…
In this paper, a class of $\log$-polyharmonic mappings $\mathcal{L}_p\mathcal{H}$ together with its subclass $\mathcal{L}_p\mathcal{H}(G)$ in the unit disk $\mathbb{D}=\{z: |z|<1\}$ is introduced, and several geometrical properties such as…
We prove an analog of the Schoen-Yau univalentness theorem for saddle maps between discs.
We prove a Liouville-type theorem for biharmonic maps from a complete Riemannian manifold of dimension \(n\) that has a lower bound on its Ricci curvature and positive injectivity radius into a Riemannian manifold whose sectional curvature…
The ordinary Landau problem consists of describing a charged particle in time-independent magnetic field. In the present case the problem is generalized onto time-dependent uniform electric fields with time-dependent mass and harmonic…
We straighten a result of [5] about arithmetic properties of the Laurent coefficients of the conformal isomorphism from the complement of the unit disk onto the complement of the Mandelbrot set. This confirms an empirical observation by Don…
We study otopy classes of equivariant local maps and prove the Hopf type theorem for such maps in the case of a real finite dimensional orthogonal representation of a compact Lie group.
The solutions of a kind of second-order homogeneous partial differential equation are called (real kernel) alpha-harmonic functions. The alpha-harmonic functions and their first-order partial derivative functions on unit disk are estimated…
For $n\geq3$, $m\geq1$ and a given continuous function $g:~\Omega\rightarrow\mathbb{R}^{m}$, we establish some Schwarz type lemmas for mappings $f$ of $\Omega$ into $\mathbb{R}^{m}$ satisfying the PDE: $\Delta f=g$, where $\Omega$ is a…
In this paper, we address several interconnected problems in the theory of harmonic maps between Riemannian manifolds. First, we present necessary background and establish one of the main results of the paper: a criterion characterizing…
In the present paper we introduce the notion of harmonicity modulus and harmonicity K-functional and apply these notions to prove a Jackson type theorem for approximation of continuous functions by polyharmonic functions. For corresponding…