M. Gaudet

Alexandrov's Theorem for Integral Varifolds and Applications to Geometric Inequalities

In this paper, we use optimal mass transportation to derive an isoperimetric inequality and an interior Michael-Simon-Sobolev inequality for weakly twice differentiable integral varifolds of dimension and codimension at least $2$, with locally bounded first variation and $L^2_{loc}$ mean curvature. This generalizes a r...