From intersection bodies to dual centroid bodies: a stochastic approach to isoperimetry

We establish a family of isoperimetric inequalities for sets that interpolate between intersection bodies and dual Lp centroid bodies. This provides a bridge between the Busemann intersection inequality and the Lutwak--Zhang inequality. The approach depends on new empirical versions of these inequalities.

From intersection bodies to dual centroid bodies: a stochastic approach to isoperimetry Institutional Repository Document