The non-parabolicity of infinite volume ends

Details The non-parabolicity of infinite volume ends The non-parabolicity of infinite volume ends

2012-01-30

arxiv.org/abs/1201.6391v1

Mathematics

Differential Geometry

Scientific paper

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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