Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing metrics on a $2$-torus with a partially prescribed stable
  norm   A result of Bangert states that the stable norm associated to any Riemannian
metric on the $2$-torus $T^2$ is strictly convex. We demonstrate that the space
of stable norms associated to metrics on $T^2$ forms a proper dense subset of
the space of strictly convex norms on $\R^2$. In particular, given a strictly
convex norm $\Norm_\infty$ on $\R^2$ we construct a sequence $<\Norm_j
>_{j=1}^{\infty}$ of stable norms that converge to $\Norm_\infty$ in the
topology of compact convergence and have the property that for each $r > 0$
there is an $N \equiv N(r)$ such that $\Norm_j$ agrees with $\Norm_\infty$ on
$\Z^2 \cap \{(a,b) : a^2 + b^2 \leq r \}$ for all $j \geq N$. Using this
result, we are able to derive results on multiplicities which arise in the
minimum length spectrum of $2$-tori and in the simple length spectrum of
hyperbolic tori.

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin