Convex functions on the Heisenberg group. (English) Zbl 1072.49019

Lu, Guozhen; Manfredi, Juan J.; Stroffolini, Bianca

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)

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