Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Triangle inequalities in path metric spaces   We study side-lengths of triangles in path metric spaces. We prove that
unless such a space X is bounded, or quasi-isometric to line or half-line,
every triple of real numbers satisfying the strict triangle inequalities, is
realized by the side-lengths of a triangle in X. We construct an example of a
complete path metric space quasi-isometric to the Euclidean plane, for which
every degenerate triangle has one side which is shorter than a certain uniform
constant.

31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin