65 citations · 125 across the 15 of their papers we have counts for
10 papers · 1 filter
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…
Grünbaum's inequality for Gaussian and convex probability measures
Matthieu Fradelizi, Dylan Langharst, Jiaqian Liu +2
A celebrated result in convex geometry is Grünbaum's inequality, which quantifies how much volume of a convex body can be cut off by a hyperplane passing through its barycenter. In…
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…
On a Santaló point for Nakamura-Tsuji's Laplace transform inequality
Dario Cordero-Erausquin, Matthieu Fradelizi, Dylan Langharst
Nakamura and Tsuji recently obtained an integral inequality involving a Laplace transform of even functions that implies, at the limit, the Blaschke-Santaló inequality in its funct…
Weighted Brunn-Minkowski Theory II: Inequalities for Mixed Measures and Applications
Matthieu Fradelizi, Dylan Langharst, Mokshay Madiman +1
In "Weighted Brunn-Minkowski Theory I", the prequel to this work, we discussed how recent developments on concavity of measures have laid the foundations of a nascent weighted Brun…
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…
The (Self-Similar, Variational) Rolling Stones
Dylan Langharst, Jacopo Ulivelli
The interplay between variational functionals and the Brunn-Minkowski Theory is a well-established phenomenon widely investigated in the last thirty years. In this work, we prove t…
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…