Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compact complete null curves in Complex 3-space   We prove that for any open orientable surface $S$ of finite topology, there
exist a Riemann surface $\mathcal{M},$ a relatively compact domain
$M\subset\mathcal{M}$ and a continuous map $X:\bar{M}\to\mathbb{C}^3$ such
that: $\mathcal{M}$ and $M$ are homeomorphic to $S,$ $\mathcal{M}-M$ and
$\mathcal{M}-\bar{M}$ contain no relatively compact components in
$\mathcal{M},$ $X|_M$ is a complete null holomorphic curve,
$X|_{\bar{M}-M}:\bar{M}-M\to\mathbb{C}^3$ is an embedding and the Hausdorff
dimension of $X(\bar{M}-M)$ is $1.$
  Moreover, for any $\epsilon>0$ and compact null holomorphic curve
$Y:N\to\mathbb{C}^3$ with non-empty boundary $Y(\partial N),$ there exist
Riemann surfaces $M$ and $\mathcal{M}$ homeomorphic to $N^\circ$ and a map
$X:\bar{M}\to\mathbb{C}^3$ in the above conditions such that
$\delta^H(Y(\partial N),X(\bar{M}-M))<\epsilon,$ where $\delta^H(\cdot,\cdot)$
means Hausdorff distance in $\mathbb{C}^3.$

23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ