The non-parabolicity of infinite volume ends

Cavalcante, M.; Mirandola, H.; Vitório, F.

doi:10.1090/S0002-9939-2014-11901-0

The non-parabolicity of infinite volume ends
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by M. P. Cavalcante, H. Mirandola and F. Vitório PDF

Proc. Amer. Math. Soc. 143 (2015), 1221-1228 Request permission

Abstract:

Let $M^m$, with $m\geq 3$, be an $m$-dimensional complete non-compact 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.

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