3 papers
math.AP2020
On the -Brunn-Minkowski and dimensional Brunn-Minkowski conjectures for log-concave measures
Johannes Hosle, Alexander V. Kolesnikov, Galyna V. Livshyts
We study several of the recent conjectures in regards to the role of symmetry in the inequalities of Brunn-Minkowski type, such as the -Brunn-Minkowski conjecture of Böröczky,…
math.MG2019
On Extensions of the Loomis-Whitney Inequality and Ball's Inequality for Concave, Homogeneous Measures
Johannes Hosle
The Loomis-Whitney inequality states that the volume of a convex body is bounded by the product of volumes of its projections onto orthogonal hyperplanes. We provide an extension o…
math.MG2018
On the Comparison of Measures of Convex Bodies via Projections and Sections
Johannes Hosle
In this manuscript, we study the inequalities between measures of convex bodies implied by comparison of their projections and sections. Recently, Giannopoulos and Koldobsky proved…