Abstract
We prove spectral, stochastic and mean curvature estimates for complete m-submanifolds φ : M → N of n-manifolds with a pole N in terms of the comparison isoperimetric ratio Im and the extrinsic radius rφ ≤ ∞. Our proof holds for the bounded case rφ < ∞, recovering the known results, as well as for the unbounded case rφ = ∞. In both cases, the fundamental ingredient in these estimates is the integrability over (0, rφ) of the inverse [Formula: see text] of the comparison isoperimetric radius. When rφ = ∞, this condition is guaranteed if N is highly negatively curved.
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