7 papers
Monotonicity formulas in positively curved settings with applications to two-phase free boundary problems
Johannes Hosle
Inspired by the monotonicity formula of Alt, Caffarelli, and Friedman, we consider a natural variant of the ACF functional in positively curved 2-dimensional settings where we inte…
The isomorphic section-projection problem for convex bodies
Johannes Hosle
Let be convex bodies in with centered. Assume that for all . We prove that , wh…
Geometric Block Exponents and a Uniform Mixed-Alphabet Sumset Inequality
Johannes Hosle, Paata Ivanisvili
We study sharp exponents in inequalities for pairs of finite geometric blocks. We characterize exactly when the endpoint determines the optimal exponent and compute the expon…
Stolarsky-Type Inequalities in a Max-Convolution Problem
Johannes Hosle
For , let . The max-convolution inequality \begin{align*} \sum_{k=0}^{2m}\left(\max_{i+j=k} x_i y_j \right)^{q_m} &\ge \left…
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,…
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…
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…