Complemented Brunn-Minkowski Inequalities and Isoperimetry for Homogeneous and Non-Homogeneous Measures

Emanuel Milman, Liran Rotem

Elementary proofs of sharp isoperimetric inequalities on a normed space $({\mathbb{R}}^n,||\cdot ||)$ equipped with a measure $\mu =w(x)dx$ so that $w^p$ is homogeneous are provided, a…