The non-parabolicity of infinite volume ends

الأصل · EN

Let Mᵐ, with m≥ 3, be an m-dimensional complete noncompact manifold isometrically immersed in a Hadamard manifold M. Assume that the mean curvature vector has finite Lᵖ-norm, for some 2≤ p≤ m. We prove that each end of M must either have finite volume or be non-parabolic.