Geodesic
On Weakly H-Quasiconvex Functions on the Heisenberg Group
Journal of convex analysis, Tome 15 (2008) no. 4, pp. 753-766

Voir la notice de l'article provenant de la source Heldermann Verlag

The aim of this paper is the investigation of weakly H-quasiconvex functions in the framework of the Heisenberg group H. The functions of this class, recently introduced by M. B. Sun and X. P. Yang ["Some properties of quasiconvex functions on the Heisenberg Group", Acta Math. Appl. Sinica 21 (2005) 571--580], are defined via the property that their sublevels are weakly H-convex subsets of H. Following Crouzeix's approach, we prove conditions of first and second order, easily testable, for regular weakly H-quasiconvex functions, and we provide a characterization of them.
Classification : 52A01, 53C17, 26B25
Mots-clés : Heisenberg group, weak H-convexity, weak H-quasiconvexity, symmetrized horizontal Hessian 
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A. Calogero; G. Carcano; R. Pini. On Weakly H-Quasiconvex Functions on the Heisenberg Group. Journal of convex analysis, Tome 15 (2008) no. 4, pp. 753-766. http://geodesic.mathdoc.fr/item/JCA_2008_15_4_JCA_2008_15_4_a5/