ar X iv : m at h / 06 10 97 9 v 1 [ m at h . D G ] 3 1 O ct 2 00 6 p - CAPACITY AND p - HYPERBOLICITY OF SUBMANIFOLDS
نویسندگان
چکیده
We use drifted Brownian motion in warped product model spaces as comparison constructions to show p-hyperbolicity of a large class of submanifolds for p ≥ 2. The condition for p-hyperbolicity is expressed in terms of upper support functions for the radial sectional curvatures of the ambient space and for the radial convexity of the sub-manifold. In the process of showing p-hyperbolicity we also obtain explicit lower bounds on the p-capacity of finite annular domains of the submanifolds in terms of the drifted 2-capacity of the corresponding annuli in the respective comparison spaces.
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