J. Haddad

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20232026

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math.MG2026

An approximate counterexample to the Barker--Larman problem in dimension $4$

J. Haddad

The Barker--Larman problem asks if a convex body $K \subseteq R^{n}$ containing the Euclidean ball $B_{n}$ , such that all the sections of $K$ by hyperplanes tangent to…

math.MG2025

Extensions of the Busemann-Petty Problem for Arbitrary Measures

Daniel Galicer, Julián Haddad, Joaquín Singer

The classical Busemann--Petty problem asks whether smaller central hyperplane sections of origin-symmetric convex bodies imply smaller total volume. Zvavitch studied the analogous…

math.MG2025

On the polar of Schneider's difference body

Julián Haddad, Dylan Langharst, Galyna V. Livshyts +1

In 1970, Schneider introduced the $m$ th-order extension of the difference body $D K$ of a convex body $K \subset R^{n}$ , the convex body $D^{m} (K)$ in $R^{nm}$ . He conject…

math.MG2024

On the volume of convolution bodies in the plane

J. Haddad

For every convex body $K \subset R^{n}$ and $δ \in (0, 1)$ , the $δ$ -convolution body of $K$ is the set of $x \in R^{n}$ for which $\left|K \cap (K+x)\right|_n \geq δ\left…

An approximate counterexample to the Barker--Larman problem in dimension 4

Extensions of the Busemann-Petty Problem for Arbitrary Measures

On the polar of Schneider's difference body

On the volume of convolution bodies in the plane

An approximate counterexample to the Barker--Larman problem in dimension $4$