Dylan Langharst

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20242026

most citedWeighted Brunn-Minkowski Theory II: Inequalities for Mixed Measures and Applications

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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

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…

math.MG2024

General Higher Order $L^{p}$ Mean Zonoids

Dylan Langharst, Dongmeng Xi

In 1970, Schneider introduced the higher-order difference body and the associated Rogers-Shephard inequality. Recently, Haddad, Langharst, Putterman, Roysdon and Ye expanded the co…

On the polar of Schneider's difference body

Higher-Order Lp Isoperimetric and Sobolev Inequalities

General Higher Order Lp Mean Zonoids

General Higher Order $L^{p}$ Mean Zonoids