In this paper we investigate the property of engulfing for H-convex functions defined on the Heisenberg group \({\mathbb {H}^n}\). Starting from the horizontal sections introduced by Capogna and Maldonado (Proc Am Math Soc 134:3191–3199, 2006) , we consider a new notion of section, called \({\mathbb {H}^n}\)-section, as well as a new condition of engulfing associated to the \({\mathbb {H}^n}\)-sections, for an H-convex function defined in \(\mathbb {H}^n.\) These sections, that arise as suitable unions of horizontal sections, are dimensionally larger; as a matter of fact, the \({\mathbb {H}^n}\)-sections, with their engulfing property, will lead to the definition of a quasi-distance in \({\mathbb {H}^n}\) in a way similar to Aimar et al. in the Euclidean case (J Fourier Anal Appl 4:377–381, 1998). 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.

在本文中，我们研究了在Heisenberg群\（{\ mathbb {H} ^ n} \）上定义的H-凸函数的卷积性质。从Capogna和Maldonado引入的水平截面开始（Proc Am Math Soc 134：3191–3199，2006），我们考虑了一个新的截面概念，称为\（{\ mathbb {H} ^ n} \）- section以及与\（{\ mathbb {H} ^ n} \）部分相关的吞噬新条件，对于\（\ mathbb {H} ^ n。\）这些部分中定义的H-凸函数，当合适的水平截面结合产生时，尺寸更大；实际上，\（{\ mathbb {H} ^ n} \）截面具有吞噬性，将以类似于Aimar等人的方式在\（{\ mathbb {H} ^ n} \）中定义准距离。在欧几里得案中（J Fourier Anal Appl 4：377-381，1998）。H凸函数的圆形H形截面的特性及其与吞没特性的联系起着关键作用。