Related papers: Compositions of polyharmonic mappings
In this article, we present univalence criteria for polyharmonic and polyanalytic functions. Our approach yields new a criterion for a polyharmonic functions to be fully $\alpha$--accessible. Several examples are presented to illustrate the…
For a polynomial map $\mathbf{f} : k^n \to k^m$ ($k$ a field), we investigate those polynomials $g \in k[t_1,\ldots, t_n]$ that can be written as a composition $g = h \circ \mathbf{f}$, where $h: k^m \to k$ is an arbitrary function. In the…
We prove that when assuming suitable non-degeneracy conditions equivariant harmonic maps into symmetric spaces of non-compact type depend in a real analytic fashion on the representation they are associated to. The main tool in the proof is…
In this paper we prove a Rad\'o type result showing that there is no univalent polyharmonic mapping of the unit disk onto the whole complex plane. We also establish a connection between the boundary functions of harmonic and biharmonic…
In this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.
In this paper, we first investigate coefficient estimates for bounded polyharmonic mappings in the unit disk $\mathbb{D}$. Then, we obtain two versions of Landau's theorem for polyharmonics mapping $F$, and for the mappings of the type…
We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then such a map is harmonic. We then give applications to…
The Harmonic Mapping Problem asks when there exists a harmonic homeomorphism between two given domains. It arises in the theory of minimal surfaces and in calculus of variations, specifically in hyperelasticity theory. We investigate this…
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…
In the present paper, we will study geometric properties of harmonic mappings whose analytic and co-analytic parts are (shifted) generated functions of completely monotone sequences.
We study a geometrical condition (PHWC) which is weaker than horizontal weak conformality. In particular, we show that harmonic maps satisfying this condition, which will be called {\em pseudoharmonic morphisms}, include harmonic morphisms…
The purpose of this paper is to study the harmonicity of maps to or from para-Sasakian manifolds. We derive the condition for the tension field of paraholomorphic map between almost para-Hermitian manifold and para-Sasakian manifold. The…
While discrete harmonic functions have been objects of interest for quite some time, this is not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of path counting problems. In this article, a novel…
On a finite graph with a chosen partition of the vertex set into interior and boundary vertices, a $\lambda$-polyharmonic function is a complex function $f$ on the vertex set which satisfies $(\lambda \cdot I - P)^n f(x) = 0$ at each…
In this paper we describe a 1-dimensional variational approach to the analytical construction of equivariant biharmonic maps. Our goal is to provide a direct method which enables analysts to compute directly the analytical conditions which…
In this article, we provide some necessary and sufficient coefficients conditions for a harmonic mapping to be hereditarily spirallike. Also, we give growth estimate for certain harmonic hereditarily spirallike mappings. Moreover, we…
We study the Lipschitz continuity of pluriharmonic Bloch mappings in the unit ball $\mathbb{B}^n$ with respect to the Bergman metric. We apply this to obtain a sufficient condition such that the composition operator on the pluriharmonic…
A weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions are introduced. Strong will imply weak. The weak concept is studied further. A function f is weakly plurifinely plurisubharmonic if and only…
In the present paper, we study bi-$f$-harmonic maps which generalize not only $f$-harmonic maps, but also biharmonic maps. We derive bi-$f$-harmonic equations for curves in the Euclidean space, unit sphere, hyperbolic space, and in…
Dirac-harmonic maps $(f,\phi)$ consist of a map $f:M\to N$ and a twisted spinor $\phi\in\Gamma(\Sigma M\otimes f^*TN)$ and they are defined as critical points of the super-symmetric energy functional. A Dirac-harmonic map is called…