Year: 2026
Type: preprint
Abstract: For planar convex bodies $A_0,A_1,A_2$ satisfying $\frac12(A_0+A_2)\subseteq A_1$, we prove that the union of the three slices $\{i\}\times A_i\subseteq\mathbb{R}^3$, $i=0,1,2$, contains a point such that every closed halfspace containing it captures at least $2/9$ of their total area. This establishes the three-slice case of Oertel's mixed-integer centerpoint conjecture in $\mathbb{Z}\times\mathbb{R}^2$ with the best possible constant.
Source: arXiv (Cornell University)
Authors: Cheng, Hongyu, Basu, Amitabh
Institution: Johns Hopkins University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3399276425
OpenAlex ID: W7214762821