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math.FA2025
Affine Isoperimetric Inequalities for Higher-Order Projection and Centroid Bodies
Julián Haddad, Dylan Langharst, Eli Putterman +2
In 1970, Schneider introduced the th order difference body of a convex body, and also established the th-order Rogers-Shephard inequality. In this paper, we extend this idea…
math.FA2024
On the -Order Weighted Projection Body Operator and Related Inequalities
Dylan Langharst, Eli Putterman, Michael Roysdon +1
For a convex body in , the inequalities of Rogers-Shephard and Zhang, written succinctly, are $$\text{vol}_n(DK)\leq \binom{2n}{n} \text{vol}_n(K) \leq \text{vol}_…