6 papers
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…
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…
On the polar of Schneider's difference body
Julián Haddad, Dylan Langharst, Galyna V. Livshyts +1
In 1970, Schneider introduced the th-order extension of the difference body of a convex body , the convex body in . He conject…
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…
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. I…
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 func…