Nonlinear p-Laplacian Comparison Theory

We use drifted Brownian motion in tailor made warped product model spaces as comparison constructions to
sudy $p$-hyperbolicity and $p$-parabolicity of a large class of submanifolds in ambient spaces with restricted
curvature behaviour. It is expected that similar techniques will also give generalized isoperimetric inequalities as well as $p$-Laplace heat kernel estimates
and mean exit time estimates for the corresponding nonlinear diffusion.