J. Haddad

collaborators

4 papers

math.FA2025

Affine Isoperimetric Inequalities for Higher-Order Projection and Centroid Bodies

JuliÃ¡n Haddad, Dylan Langharst, Eli Putterman +2

In 1970, Schneider introduced the $m$ th order difference body of a convex body, and also established the $m$ th-order Rogers-Shephard inequality. In this paper, we extend this idea…

math.MG2025

Affine Fractional Sobolev and Isoperimetric Inequalities

JuliÃ¡n Haddad, Monika Ludwig

Sharp affine fractional Sobolev inequalities for functions on $R^{n}$ are established. For each $0 < s < 1$ , the new inequalities are significantly stronger than (and directly im…

math.FA2024

A Rogers--Brascamp--Lieb--Luttinger inequality in the space of matrices

JuliÃ¡n Haddad

We consider convex bodies in $M_{n, m} (R)$ , the space of matrices of $n$ -rows and $m$ -columns. A special case of fiber-symmetrization in $M_{n, m} (R)$ was recently in…

math.MG2024

Higher-Order Lp Isoperimetric and Sobolev Inequalities

JuliÃ¡n Haddad, Dylan Langharst, Eli Putterman +2

Schneider introduced an inter-dimensional difference body operator on convex bodies and proved an associated inequality. In the prequel to this work, we showed that this concept ca…