5 papers · 1 filter
Affine isoperimetric inequalities for the first eigenvalue of the -th order Affine -Laplace Operator
Dylan Langharst, Michael Roysdon
Recently, Haddad, Jiménez, and Montenegro introduced the affine -Laplace operator, , and studied associated affine versions of the isoperimetric inequalities for the first…
Functional Liftings of Restricted Geometric Inequalities
Andreas Malliaris, James Melbourne, Cyril Roberto +1
We investigate what we term "generalized sup-convolutions". We show that functional inequalities that enjoy an interpretation as sup-convolution inequalities can be deduced from th…
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…
On the th-order Affine Pólya-Szegö Principle
Dylan Langharst, Michael Roysdon, Yiming Zhao
An affine Pólya-Szegö principle for a family of affine energies, with equality condition characterization, is demonstrated. In particular, this recovers, as special cases, the $L…
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}_…