12 citations · 12 across the 5 of their papers we have counts for
8 papers
The Bézout inequality for mixed volumes characterizes simplices
Dylan Langharst, Shouda Wang
We prove that the Bézout inequality for mixed volumes characterizes simplices among full dimensional convex bodies in every dimension, resolving a conjecture of Soprunov and Zvavit…
Convexity of Radial Mean Bodies via an Extension of Ball's Bodies
Dylan Langharst
In this work, we extend a classical theorem of Keith Ball on integrals of log-concave functions along rays against the weight to the previously inaccessible regime $p\in…
On the Fourier Mean Bodies of a Convex Body
Dylan Langharst, Auttawich Manui, Artem Zvavitch
In 1998, R. Gardner and G. Zhang introduced the radial th mean bodies of a convex body , , which have since become important objects in geometr…
Some comments on the mth-order Projection Bodies
Dylan Langharst
The celebrated Petty's projection inequality is a sharp upper bound for the volume of the polar projection body of a convex body. Lutwak introduced the concept of mixed projection…
On Moment-Entropy inequalities in the space of matrices
Dylan Langharst
In a series of works, Lutwak, Yang and Zhang established what could be called affine information theory, which is the study of moment-entropy and Fisher-information-type inequaliti…
The Weighted Minkowski Problem
Dylan Langharst, Jiaqian Liu, Shengyu Tang
The Minkowski problem in convex geometry concerns showing that a given Borel measure on the unit sphere is, up to perhaps a constant, some type of surface area measure of a convex…
Higher-Order Reverse Isoperimetric Inequalities for Log-concave Functions
Dylan Langharst, Francisco Marín Sola, Jacopo Ulivelli
The Rogers-Shephard and Zhang's projection inequalities are two reverse, affine isoperimetric-type inequalities for convex bodies. Following a classical work by Schneider, both ine…
Weighted Minkowski's Existence Theorem and Projection Bodies
Liudmyla Kryvonos, Dylan Langharst
The Brunn-Minkowski Theory has seen several generalizations over the past century. Many of the core ideas have been generalized to measures. With the goal of framing these generali…