Geodesic diameter of sets defined by few quadratic equations and inequalities

Michel Coste (1) , Seydou Moussa (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Département de Mathématiques

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).

Mots clés: semialgebraic set; geodesic diameter; quadratic equations

Domaines: Géométrie algébrique [math.AG]

Michel Coste, Seydou Moussa. Geodesic diameter of sets defined by few quadratic equations and inequalities. Mathematische Zeitschrift, 2012, 272 (1), pp.239-251. ⟨10.1007/s00209-011-0931-6⟩. ⟨hal-00514488⟩