12 citations · 12 across the 5 of their papers we have counts for
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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…
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…