Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The non-parabolicity of infinite volume ends   Let $M^m$, with $m\geq 3$, be an $m$-dimensional complete noncompact manifold
isometrically immersed in a Hadamard manifold $\bar M$. Assume that the mean
curvature vector has finite $L^p$-norm, for some $2\leq p\leq m$. We prove that
each end of $M$ must either have finite volume or be non-parabolic.

21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
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The categories of this paper are: eess