New properties of convex functions in the Heisenberg group
New properties of convex functions in the Heisenberg group
We prove some new properties of the weakly $H$-convex functions recently introduced by Danielli, Garofalo and Nhieu. As an interesting application of our results we prove a theorem of Busemann-Feller-Alexandrov type in the Heisenberg groups $\mathbb {H}^n$, $n=1,2$.