2020/07/21 by Andrea Calogero, Calogero, Andrea, R. Pini +1
Mathematics · #26A12 #26B25 #52A30 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2007.11068
openalex publication_date 2020/07/21 · openalex created_date 2020/07/29 · openalex updated_date 2026/07/28
In this paper we investigate the property of engulfing for H-convex functions defined on the Heisenberg group ℍn. Starting from the horizontal sections introduced by Capogna and Maldonado, we consider a new notion of section, called ℍn-section, as well as a new condition of engulfing associated to the ℍn-sections, for an H-convex function defined in ℍn. These sections, that arise as suitable unions of horizontal sections, are dimensionally larger; as a matter of fact, the ℍn-sections, with their engulfing property, will lead to the definition of a pseudo-metric in ℍn in a way similar to Aimar, Forzani and Toledano in the Euclidean case. A key role is played by the property of round H-sections for an H-convex function, and by its connection with the engulfing properties.