Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedded minimal surfaces in $\mathbb{R}^n$   In this paper, we prove that every confomal minimal immersion of an open
Riemann surface into $\mathbb{R}^n$ for $n\ge 5$ can be approximated uniformly
on compacts by conformal minimal embeddings. Furthermore, we show that every
open Riemann surface carries a proper conformal minimal embedding into
$\mathbb{R}^5$. One of our main tools is a Mergelyan approximation theorem for
conformal minimal immersions to $\mathbb{R}^n$ for any $n\ge 3$ which is also
proved in the paper.

17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg