Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior of Vianna's exotic Lagrangian tori $T_{a,b,c}$ in
  $\mathbb{CP}^2$ as $a+b+c \to \infty$   In this paper, we study various asymptotic behavior of the infinite family of
monotone Lagrangian tori $T_{a,b,c}$ in $\mathbb{CP}^2$ associated to Markov
triples $(a,b,c)$ described in \cite{Vi14}. We first prove that the Gromov
capacity of the complement $\mathbb{CP}^2 \setminus T_{a,b,c}$ is greater than
or equal to $\frac13$ of the area of the complex line for all Markov triple
$(a,b,c)$. We then prove that there is a representative of the family
$\{T_{a,b,c}\}$ whose loci completely miss a metric ball of nonzero size and in
particular the loci of the union of the family is not dense in $\mathbb{CP}^2$.

33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol