16 citations · 38 across the 12 of their papers we have counts for
13 papers
On cost-induced Santaló-type inequalities in Polish measure spaces
Dylan Langharst, Andreas Malliaris, Michael Roysdon
We introduce a framework for establishing Blaschke-Santaló-type inequalities on -tuples of Polish measure spaces coupled together by a continuous cost function. Central to our a…
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…
From simplex slicing to sharp reverse Hölder inequalities
James Melbourne, Michael Roysdon, Colin Tang +1
Simplex slicing (Webb, 1996) is a sharp upper bound on the volume of central hyperplane sections of the regular simplex. We extend this to sharp bounds in the probabilistic framewo…
A Busemann-Petty Type Problem for Dual Radon Transforms
Michael Roysdon
Inspired by resolution of the Busemann-Petty problem (1956), we consider the following comparison problem for dual Radon transforms: Given a pair of continuous functions defined on…
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^p…
Comparison Problems for Radon Transforms
Alexander Koldobsky, Michael Roysdon, Artem Zvavitch
Given two non-negative functions and such that the Radon transform of is pointwise smaller than the Radon transform of , does it follow that the -norm of is…
Higher-Order Lp Isoperimetric and Sobolev Inequalities
Julián 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…
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}_…
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…
General Measure Extensions of Projection Bodies
Dylan Langharst, Michael Roysdon, Artem Zvavitch
The inequalities of Petty and Zhang are affine isoperimetric-type inequalities providing sharp bounds for where is a projecti…
Rogers-Shepard Type Inequalities for Sections
Michael Roysdon
In this paper we address the following question: given a measure on , does there exists a constant such that, for any -dimensional subspace $H \subset \m…
On Rogers-Shephard type inequalities for general measures
David Alonso-Gutiérrez, María A. Hernández Cifre, Michael Roysdon +2
In this paper we prove a series of Rogers-Shephard type inequalities for convex bodies when dealing with measures on the Euclidean space with either radially decreasing densities,…