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28 March 2024
 
  » arxiv » math.DG/0203203

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L-convex-concave sets in real projective space and L-duality
A. Khovanskii ; D. Novikov ;
Date 19 Mar 2002
Subject Differential Geometry; Classical Analysis and ODEs MSC-class: 52A30; 26B25, 52A37 | math.DG math.CA
AbstractWe define a class of L-convex-concave subsets of $Bbb{R}P^n$, where L is a projective subspace of dimension l in $Bbb{R}P^n$. These are sets whose sections by any (l+1)-dimensional space L’ containing L are convex and concavely depend on L’. We introduce an L-duality for these sets, and prove that the L-dual to an L-convex-concave set is an $L^*$-convex-concave subset of $(Bbb RP^n)^*$. We discuss a version of Arnold hypothesis for these sets and prove that it is true (or wrong) for an L-convex-concave set and its L-dual simultaneously.
Source arXiv, math.DG/0203203
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