English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper we investigate the property of engulfing for $H$-convexfunctions defined on the Heisenberg group ${\mathbb{H}}^n$. Starting from thehorizontal sections introduced by Capogna and Maldonado, we consider a newnotion of section, called ${\mathbb{H}}^n$-section, as well as a new conditionof engulfing associated to the ${\mathbb{H}}^n$-sections, for an $H$-convexfunction defined in ${\mathbb{H}}^n.$ These sections, that arise as suitableunions of horizontal sections, are dimensionally larger; as a matter of fact,the ${\mathbb{H}}^n$-sections, with their engulfing property, will lead to thedefinition of a pseudo-metric in ${\mathbb{H}}^n$ in a way similar to Aimar,Forzani and Toledano in the Euclidean case. A key role is played by theproperty of round $H$-sections for an $H$-convex function, and by itsconnection with the engulfing properties.

The engulfing property for sections of convex functions in the Heisenberg group and the associated quasi--metric