L-convex-concave sets in real projective space and L-duality
| dc.creator | Khovanskii, A. | |
| dc.creator | Novikov, D. | |
| dc.date | 2002-03-19 | |
| dc.date.accessioned | 2026-07-07T04:47:11Z | |
| dc.date.available | 2026-07-07T04:47:11Z | |
| dc.description | We 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.description | 23pp | |
| dc.identifier | https://arxiv.org/abs/math/0203203 | |
| dc.identifier | http://arxiv.org/abs/math/0203203 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63610 | |
| dc.subject | Differential Geometry | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 52A30; 26B25, 52A37 | |
| dc.title | L-convex-concave sets in real projective space and L-duality | |
| dc.type | text |