Abstract

In this paper, we prove that integral $n$-varifolds $\mu $ in codimension 1 with $H_\mu \in L^p_{\mathrm{loc}\nolimits } $, $p > n$, $p \ge 2$ have quadratic tilt-excess decay $\mathrm{tiltex}_\mu = O_x$for $\mu $-almost all $x$, and a strong maximum principle which states that these varifolds cannot be touched by smooth manifolds whose mean curvature is given by the weak mean curvature $H_\mu $, unless the smooth manifold is locally contained in the support of $\mu $