Mean time exit and isoperimetric inequalities for minimal submanifolds of Nx

Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities, we establish a slightly better isoperimetric inequality and mean time exit estimates for minimal submanifolds of N x when N is non-positively curved. We prove isoperimetric inequalities for submanifolds with tamed second fundamental form in Hadamard spaces with bounded sectional curvature. We use mean time exit functions to show that spherically symmetric manifolds with geodesic spheres with exponential volume growth have a positive first eigenvalue.