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A centerpoint theorem for three planar convex bodies — arXiv:2609.32953

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.32953
License (as archived): CC0-1.0
Archived: 2026-10-07T23:06:53.737Z
SHA-256 of the archived text: 9a9fd5a7ab6c715147e7660eed7acb216ca7a2d9e8cdbe17c2982ee5751f1160
Stable URL of this page: https://metraipolis.com/documento/dc_ec6ecf8bfa39

How to cite

A centerpoint theorem for three planar convex bodies — arXiv:2609.32953 — arXiv (en), https://arxiv.org/abs/2609.32953 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ec6ecf8bfa39 (Metraipolis archive dc_ec6ecf8bfa39, sha256 9a9fd5a7ab6c715147e7660eed7acb216ca7a2d9e8cdbe17c2982ee5751f1160)

BibTeX

@misc{dcec6ecf8bfa39,
  title = {A centerpoint theorem for three planar convex bodies — arXiv:2609.32953},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.32953},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ec6ecf8bfa39; sha256 9a9fd5a7ab6c715147e7660eed7acb216ca7a2d9e8cdbe17c2982ee5751f1160},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.32953. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-29 in math.OC).
Categorie arXiv: Metric Geometry (math.MG) ; Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2609.32953 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T22:42:39.309Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).