Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally one-to-one harmonic functions with starlike analytic part   Let $L_H$ denote the set of all normalized locally one-to-one and
sense-preserving harmonic functions in the unit disc $\Delta$. It is well-known
that every complex-valued harmonic function in the unit disc $\Delta$ can be
uniquely represented as $f = h + \overline{g}$, where $h$ and $g$ are analytic
in $\Delta$. In particular the decomposition formula holds true for functions
of the class $L_H$. For a fixed analytic function $h$, an interesting problem
arises - to describe all functions $g$, such that $f$ belongs to $L_H$.
  The case when $f\in L_H$ and $h$ is the identity mapping was considered [2].
More general results are given in [3], where $f\in L_H$ and letting $h$ to be a
convex analytic mapping. The focus of our present research is to characterize
the set of all functions $f\in L_H$ having starlike analytic part $h$. In this
paper, we provide coefficient, distortion and growth estimates of $g$. We also
give growth and Jacobian estimates of $f$.

31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph