Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous boundary values of conformal maps   Let $G$ be a bounded simply connected domain in the complex plane. A point
$a\in \partial G$ is said to be accessible from inside of $G$ if there is a
Jordan arc $J$ such that $J\subset \bar G$ and $J\cap\partial G=\{a\}$. In this
paper the author shows that a univalent analytic function $\psi$ from the unit
disk $D$ onto $G$ extends continuously to $\bar D$ if and only if every
$a\in\partial G$ is accessible. The main result covers a famous theorem proved
by C. Carathe\"{o}dory, which says that if $G$ is a Jordan domain, then $\psi$
extends to be a homeomorphism from $\bar D$ onto to $\bar G$.

8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc