Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the injectivity radius and tangent cones at infinity of gradient
  Ricci solitons   A lower-bound estimate of injectivity radius for complete Riemannian
manifolds is discussed in a pure geometric viewpoint and is applied to study
tangent cones at infinity of certain gradient Ricci solitons. We also study the
asymptotic volume ratio of gradient Ricci solitons.

6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol