L-convex-concave sets in real projective space and L-duality

dc.creatorKhovanskii, A.
dc.creatorNovikov, D.
dc.date2002-03-19
dc.date.accessioned2026-07-07T04:47:11Z
dc.date.available2026-07-07T04:47:11Z
dc.descriptionWe 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.
dc.description23pp
dc.identifierhttps://arxiv.org/abs/math/0203203
dc.identifierhttp://arxiv.org/abs/math/0203203
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63610
dc.subjectDifferential Geometry
dc.subjectClassical Analysis and ODEs
dc.subject52A30; 26B25, 52A37
dc.titleL-convex-concave sets in real projective space and L-duality
dc.typetext

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