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 
@article{JCA_2008_15_4_JCA_2008_15_4_a5,
     author = {A. Calogero and G. Carcano and R. Pini},
     title = {On {Weakly} {H-Quasiconvex} {Functions} on the {Heisenberg} {Group}},
     journal = {Journal of convex analysis},
     pages = {753--766},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JCA_2008_15_4_JCA_2008_15_4_a5/}
}
TY  - JOUR
AU  - A. Calogero
AU  - G. Carcano
AU  - R. Pini
TI  - On Weakly H-Quasiconvex Functions on the Heisenberg Group
JO  - Journal of convex analysis
PY  - 2008
SP  - 753
EP  - 766
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2008_15_4_JCA_2008_15_4_a5/
ID  - JCA_2008_15_4_JCA_2008_15_4_a5
ER  - 
%0 Journal Article
%A A. Calogero
%A G. Carcano
%A R. Pini
%T On Weakly H-Quasiconvex Functions on the Heisenberg Group
%J Journal of convex analysis
%D 2008
%P 753-766
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2008_15_4_JCA_2008_15_4_a5/
%F JCA_2008_15_4_JCA_2008_15_4_a5
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/