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

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
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