J. Haddad

activity

20242026

collaborators

3 papers

math.MG2026

Extensions of the Busemann-Petty Problem for Arbitrary Measures

Daniel Galicer, JuliÃ¡n Haddad, JoaquÃn Singer

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

math.MG2025

On the polar of Schneider's difference body

JuliÃ¡n 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 $I^´ \in (0, 1)$ , the $I^´$ -convolution body of $K$ is the set of $x \in R^{n}$ for which $\left|K \cap (K+x)\right|_n \geq Î´\l…