Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On sufficient conditions to extend Huber's finite connectivity theorem
  to higher dimensions   Let $M$ be a connected complete noncompact $n$-dimensional Riemannian
manifold with a base point $p \in M$ whose radial sectional curvature at $p$ is
bounded from below by that of a noncompact surface of revolution which admits a
finite total curvature where $n \geq 2$. Note here that our radial curvatures
can change signs wildly. We then show that $\lim_{t\to\infty} \mathrm{vol}
B_t(p) / t^n$ exists where $\mathrm{vol} B_t(p)$ denotes the volume of the open
metric ball $B_t(p)$ with center $p$ and radius $t$. Moreover we show that in
addition if the limit above is positive, then $M$ has finite topological type
and there is therefore a finitely upper bound on the number of ends of $M$.

1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th