We consider the notion of H-subdifferential and H-normal map of a function u on the Heisenberg group, based on the sub-Riemannian structure. The aim of this paper is to show how these objects, like in the Euclidean setting, fit well in the investigation of a function. In particular, a characterization of the convexity can be given via the nonemptiness of the H-subdifferential at every point g; furthermore, a convex function can be recovered through a well-known Rockafellar integration result adapted to the structure of the Heisenberg group. Moreover, we prove a monotonicity result for the H-normal map when a suitable strictly convex radial function u is considered, and we suggest a definition of the Monge-Ampère measure of a function v via the horizontal subgradient of v

Calogero, A., Pini, R. (2011). Horizontal normal map on the Heisenberg group. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 12(2), 287-307.

Horizontal normal map on the Heisenberg group

CALOGERO, ANDREA GIOVANNI;PINI, RITA
2011

Abstract

We consider the notion of H-subdifferential and H-normal map of a function u on the Heisenberg group, based on the sub-Riemannian structure. The aim of this paper is to show how these objects, like in the Euclidean setting, fit well in the investigation of a function. In particular, a characterization of the convexity can be given via the nonemptiness of the H-subdifferential at every point g; furthermore, a convex function can be recovered through a well-known Rockafellar integration result adapted to the structure of the Heisenberg group. Moreover, we prove a monotonicity result for the H-normal map when a suitable strictly convex radial function u is considered, and we suggest a definition of the Monge-Ampère measure of a function v via the horizontal subgradient of v
Articolo in rivista - Articolo scientifico
Heisenberg group, convex function, horizontal subdifferential, horizontal normal map, Monge-Ampère measure, Rockafellar function
English
2011
12
2
287
307
none
Calogero, A., Pini, R. (2011). Horizontal normal map on the Heisenberg group. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 12(2), 287-307.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/24568
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