New properties of convex functions in the Heisenberg group

Garofalo, Nicola; Tournier, Federico

doi:10.1090/S0002-9947-05-04016-X

New properties of convex functions in the Heisenberg group
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by Nicola Garofalo and Federico Tournier PDF

Trans. Amer. Math. Soc. 358 (2006), 2011-2055 Request permission

Abstract:

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 $\mathbb {H}^n$, $n=1,2$.

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