Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the metric geometry of the space of compact balls and the shooting
  property for length spaces   In this work we study the geodesic structure of the space $\Sigma (X)$ of
compact balls of a complete and locally compact metric length space endowed
with the Hausdorff distance $d_H$. In particular, we focus on a geometric
condition (referred to as the shooting property) that enables us to give an
explicit isometry between $(\Sigma (X),d_H)$ and the closed half-space $
X\times \mathbb{R}_{\ge 0}$ endowed with a taxicab metric.

33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th