Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on the topology and index of minimal surfaces   We prove that for every nonnegative integer $g$, there exists a bound on the
number of ends of a complete, embedded minimal surface $M$ in $\mathbb{R}^3$ of
genus $g$ and finite topology. This bound on the finite number of ends when $M$
has at least two ends implies that $M$ has finite stability index which is
bounded by a constant that only depends on its genus.

13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs