J. Haddad

activity

20232026

collaborators

5 papers

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…

math.FA2023

Radon transforms with small derivatives and distance inequalities for convex bodies

Julián Haddad, Alexander Koldobsky

Generalizing the slicing inequality for functions on convex bodies from [11], it was proved in [4] that there exists an absolute constant $c$ so that for any $n \in N$ , any…

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

Radon transforms with small derivatives and distance inequalities for convex bodies

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