Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strongly Contracting Geodesics in a Tree of Spaces   Let X be a tree of proper geodesic spaces with edge spaces strongly
contracting and uniformly separated from each other by a number depending on
the contraction function of edge spaces. Then we prove that the strongly
contracting geodesics in vertex spaces are quasiconvex in X. We further prove
that in X if all the vertex spaces are uniformly hyperbolic metric spaces then
X is a hyperbolic metric space and vertex spaces are quasiconvex in X.

35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th