  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.

Differential Geometry