Related papers: Sections of univalent harmonic mappings
In this paper our aim is to determine the radii of univalence, starlikeness and convexity of the normalized regular Coulomb wave functions for two different kinds of normalization. The key tools in the proof of our main results are the…
In this paper, we define a subclass of sense-preserving harmonic functions associated with a class of analytic functions satisfying a differential inequality. We then establish a close relation between both subclasses. Further, we obtain…
In this article, we construct generalized harmonic univalent mappings and find its coefficients bounds. We present the counterexample to validate the coefficient conjecture proposed by Clunie and Sheil-Small for the class of functions…
The Bohr radius for the class of harmonic functions of the form $ f(z)=h+\overline{g} $ in the unit disk $ \mathbb{D}:=\{z\in\mathbb{C} : |z|<1\} $, where $ h(z)=\sum_{n=0}^{\infty}a_nz^n $ and $ g(z)=\sum_{n=1}^{\infty}b_nz^n $ is to find…
In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
We present a result on existence of some kind of peak functions for $\C$-convex domains and for the symmetrized polydisc. Then we apply the latter result to show the equivariance of the set of peak points for $A(D)$ under proper holomorphic…
We consider the class of all sense-preserving harmonic mappings $f= h+\overline{g}$ of the unit disk $\ID$, where $h$ and $g$ are analytic with $g(0)=0$, and determine the Bohr radius if any one of the following conditions holds: \bee $h$…
For a given set of $n\times n$ matrices $\mathcal F$, we study the union of the $C$-numerical ranges of the matrices in the set $\mathcal F$, denoted by $W_C({\mathcal F})$. We obtain basic algebraic and topological properties of…
We prove some sharp inequalities for complex harmonic functions on the unit disk. The results extend a M. Riesz conjugate function theorem and some well-known estimates for holomorphic functions. We apply some of results to the…
Estimates on the initial coefficients are obtained for normalized analytic functions $f$ in the open unit disk with $f$ and its inverse $g=f^{-1}$ satisfying the conditions that $zf'(z)/f(z)$ and $zg'(z)/g(z)$ are both subordinate to a…
In this paper, we will study the partial regularity theorem for stationary harmonic maps from a Riemannian manifold into a Lorentzian manifold. For a weakly stationary harmonic map $(u,v)$ from a smooth bounded open domain…
If $f=u+iv$ is analytic in the unit disk $\mathbb{D}$, it is known that the integral means $M_p(r,u)$ and $M_p(r,v)$ have the same order of growth. This is false if $f$ is a (complex-valued) harmonic function. However, we prove that the…
In this paper we determine the radius of convexity for three kind of normalized Bessel functions of the first kind. In the mentioned cases the normalized Bessel functions are starlike-univalent and convex-univalent, respectively, on the…
The radius of convexity of two normalized Bessel functions of the first kind are determined in the case when the order is between $-2$ and $-1.$ Our methods include the minimum principle for harmonic functions, the Hadamard factorization of…
The article contains several observations on spherical harmonics and their nodal sets: a construction for harmonics with prescribed zeroes; a kind of canonical representation of this type for harmonics on $\bbS^2$; upper and lower bounds…
The convex shape contained in a disk having prescribed area and maximal perimeter is completely characterized in terms of the area fraction. The solution is always a polygon having all but one sides equal. The lengths of the sides are…
We prove that a quasiisometric map between rank one symmetric spaces is within bounded distance from a unique harmonic map. In particular, this completes the proof of the Schoen-Li-Wang conjecture.
In this investigation our main aim is to determine the radius of uniform convexity of the some normalized q-Bessel and Wright functions. Here we consider six different normalized forms of q-Bessel functions, while we apply three different…
We investigate properties of ($\alpha,\beta$)-harmonic functions. First, we discuss the coefficient estimates for ($\alpha,\beta$)-harmonic functions. In particular, we obtain Heinz's inequality for ($\alpha,\beta$)-harmonic functions,…
A general criterion in terms of the Schwarzian derivative is given for global univalence of the Weierstrass--Enneper lift of a planar harmonic mapping. Results on distortion and boundary regularity are also deduced. Examples are given to…