Dylan Langharst

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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…

math.MG2025

Higher-Order Reverse Isoperimetric Inequalities for Log-concave Functions

Dylan Langharst, Francisco MarÃn 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…