Lu, Guozhen; Manfredi, Juan J.; Stroffolini, Bianca Convex functions on the Heisenberg group. (English) Zbl 1072.49019 Calc. Var. Partial Differ. Equ. 19, No. 1, 1-22 (2004). Convexity is certainly a very important property in many fields. To develop an intrinsic theory of fully nonlinear subelliptic equations, the authors of this paper discuss convexities of functions on the Heisenberg group. Group convexity, horizontal convexity and viscosity convexity are considered. Some basic and interesting properties about convex functions are given. Reviewer: Hongwei Lou (Shanghai) Cited in 45 Documents MSC: 49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games 35J70 Degenerate elliptic equations 22E30 Analysis on real and complex Lie groups 35J60 Nonlinear elliptic equations 26B25 Convexity of real functions of several variables, generalizations Keywords:convex functions; Heisenberg group; fully nonlinear subelliptic equations; viscosity convexity; horizontal convexity PDF BibTeX XML Cite \textit{G. Lu} et al., Calc. Var. Partial Differ. Equ. 19, No. 1, 1--22 (2004; Zbl 1072.49019) Full Text: DOI