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arXiv · 2304.00794

Complex $L_p$-Intersection Bodies

Simon Ellmeyer·Georg C. Hofstätter
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Abstract

Interpolating between the classic notions of intersection and polar centroid bodies, (real) $L_p$-intersection bodies, for $-1 -2$, is introduced, interpolating between complex intersection and polar complex centroid bodies. It is shown that the complex $L_p$-intersection body of an $\mathbb{S}^1$-invariant convex body is pseudo-convex, if $-2<p<-1$ and convex, if $p\geq-1$. Moreover, intersection inequalities of Busemann--Petty type in the sense of Adamczak--Paouris--Pivovarov--Simanjuntak are deduced.

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Simon Ellmeyer, Georg C. Hofstätter. 2023-04-03. Complex $L_p$-Intersection Bodies. https://arxiv.org/abs/2304.00794

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