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Convex-concave body in $\mathbb{R}P^3$ contains a line

A. Khovanskii·D. Novikov
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Abstract

We define a class of $L$-convex-concave subsets of $\mathbb{R}P^3$, where $L$ is a projective line in $\mathbb{R}P^3$. These are sets whose sections by any plane containing $L$ are convex and concavely depend on this plane. We prove a version of Arnold hypothesis for these sets, namely we prove that each such set contains a line.

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A. Khovanskii, D. Novikov. 2002-03-19. Convex-concave body in $\mathbb{R}P^3$ contains a line. https://arxiv.org/abs/math/0203200

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