Johannes Hosle

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20182026

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math.MG2026

The isomorphic section-projection problem for convex bodies

Johannes Hosle

Let $K, L$ be convex bodies in $R^{n}$ with $K$ centered. Assume that $∣ K \cap θ^{⊥} ∣ \leq ∣ L ∣ θ^{⊥} ∣$ for all $θ \in S^{n - 1}$ . We prove that $∣ K ∣ \leq c n ∣ L ∣$ , wh…

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…