A sharp lower bound on the mean curvature integral with critical power for integral varifolds

Part I Weakly differentiable functions Part II PDEs on varifolds 15 Sobolev spaces … 75 16 Preliminaries … 82 17 Maximum estimates … 86 18 Second order flatness of Lebesgue spaces for integral varifolds with subcritical integrability of the mean curvature … 94 19 Second order differentiability of the support of integral varifolds with critical integrability of the mean curvature … 100 20 Harnack inequality … 108 Part III The generalised Gauss map 21 Points of finite lower density … 118 22 Points of infinite density … 130 23 Area formula for the generalised Gauss map … 137 24 A sharp lower bound on the mean curvature integral with critical power for integral varifolds … 138 Appendix A Monotonicity identity … 139 B An observation concerning the Lusin property … 140