Dylan Langharst

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20212026

most citedWeighted Minkowski's Existence Theorem and Projection Bodies

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

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math.MG2026

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…

math.MG2026

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 $r^{p - 1}$ to the previously inaccessible regime $p\in…

math.MG2026

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 $p$ th mean bodies $R_{p} K$ of a convex body $K \subset R^{n}$ , $p > - 1$ , which have since become important objects in geometr…