A sharp quantitative estimate for the surface areas of convex sets in $\mathbb R^3$
A sharp quantitative estimate for the surface areas of convex sets in $\mathbb R^3$
Let E \subset B \subset \mathbb R^3 be closed, bounded, convex sets. It is known that the monotonicity of the surface areas holds, i.e. \mathcal{H}^{2}(\partial E) \leqslant \mathcal{H}^{2}(\partial B) . Here we give a quantitative estimate of the difference of the surface areas from below depending on the Hausdorff distance …