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| HAL : hal-00514488, version 1 |
| arXiv : 1009.0452 |
| DOI : 10.1007/s00209-011-0931-6 |
| Fiche détaillée |  Récupérer au format |
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| Mathematische Zeitschrift 272, 1 (2012) 239-251 |
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| Geodesic diameter of sets defined by few quadratic equations and inequalities |
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| Michel Coste 1Seydou Moussa 2 |
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| (2012) |
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| We prove a bound for the geodesic diameter of a subset of the unit ball in $\mathbb{R}^n$ described by a fixed number of quadratic equations and inequalities, which is polynomial in $n$, whereas the known bound for general degree is exponential in $n$. Our proof uses methods borrowed from D'Acunto and Kurdyka (to deal with the geodesic diameter) and from Barvinok (to take advantage of the quadratic nature). |
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| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2 : | Département de Mathématiques |
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Université Abdou Moumouni |
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| Domaine | : | Mathématiques/Géométrie algébrique |
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| semialgebraic set – geodesic diameter – quadratic equations |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00514488, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00514488 | |
| oai:hal.archives-ouvertes.fr:hal-00514488 | |
| Contributeur : Michel Coste | |
| Soumis le : Jeudi 2 Septembre 2010, 15:40:19 | |
| Dernière modification le : Mardi 25 Septembre 2012, 11:57:45 | |
