Stochastic reverse isoperimetric inequalities in the plane

Abstract

In recent years, it has been shown that some classical inequalities follow from a local stochastic dominance for naturally associated random polytopes. We strengthen planar isoperimetric inequalities by attaching a stochastic model to some classical inequalities, such as Mahler's Theorem, and a reverse Lutwak-Zhang inequality, the polar for $L_p$ centroid bodies. In particular, we obtain the dual counterpart to a result of Bisztriczky-Böröczky.

References in corpus (2)

• Mahler's conjecture for some hyperplane sections
• On symmetric versions of Sylvester's problem