TY - JOUR

T1 - Comparison of exit time moment spectra for extrinsic metric balls

A1 - Hurtado,Ana

A1 - Markvorsen,Steen

A1 - Palmer,Vicente

AU - Hurtado,Ana

AU - Markvorsen,Steen

AU - Palmer,Vicente

PB - Springer Netherlands

PY - 2012

Y1 - 2012

N2 - We prove explicit upper and lower bounds for the $L^1$-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds $P^m$ in ambient Riemannian spaces $N^n$. 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 $N^n$ themselves.

AB - We prove explicit upper and lower bounds for the $L^1$-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds $P^m$ in ambient Riemannian spaces $N^n$. 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 $N^n$ themselves.

KW - Exit moment spectrum

KW - Torsional rigidity

KW - Riemannian submanifolds

U2 - 10.1007/s11118-011-9223-3

DO - 10.1007/s11118-011-9223-3

JO - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

IS - 1

VL - 36

SP - 137

EP - 153

ER -