Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hedlund-Metrics and the Stable Norm   The real homology of a compact Riemannian manifold $M$ is naturally endowed
with the stable norm. The stable norm on $H_1(M,\mathbb{R})$ arises from the
Riemannian length functional by homogenization. It is difficult and interesting
to decide which norms on the finite-dimensional vector space
$H_1(M,\mathbb{R})$ are stable norms of a Riemannian metric on $M$. If the
dimension of $M$ is at least three, I. Babenko and F. Balacheff proved in
\cite{baba} that every polyhedral norm ball in $H_1(M,\mathbb{R})$, whose
vertices are rational with respect to the lattice of integer classes in
$H_1(M,\mathbb{R})$, is the stable norm ball of a Riemannian metric on $M$.
This metric can even be chosen to be conformally equivalent to any given
metric. The proof in \cite{baba} uses singular Riemannian metrics on polyhedra
which are finally smoothed. Here we present an alternative construction of such
metrics which remains in the geometric framework of smooth Riemannian metrics.

15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci