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arXiv · 1201.6391

The non-parabolicity of infinite volume ends

Marcos P. Cavalcante·Heudson Mirandola·Feliciano Vitorio
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Abstract

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.

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Marcos P. Cavalcante, Heudson Mirandola, Feliciano Vitorio. 2013-04-13. The non-parabolicity of infinite volume ends. https://arxiv.org/abs/1201.6391

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