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Comparison of exit time moment spectra for extrinsic metric balls
We prove explicit upper and lower bounds for the L1-moment spectra for
the Brownian motion exit time from extrinsic metric balls of submanifolds Pm in
ambient Riemannian spaces Nn. We assume that P and N both have controlled
radial curvatures (mean curvature and sectional curvature, respectively) as viewed from a pole in N. The bounds for the exit moment spectra are given in terms of the corresponding spectra for geodesic metric balls in suitably warped product model spaces. The bounds are sharp in the sense that equalities are obtained in characteristic cases. As a corollary we also obtain new intrinsic comparison results for the exit time spectra for metric balls in the ambient manifolds Nn themselves