论文标题
Heisenberg组和相关的准仪表中凸功能部分的吞噬属性
The engulfing property for sections of convex functions in the Heisenberg group and the associated quasi--metric
论文作者
论文摘要
在本文中，我们研究了Heisenberg Group $ {\ Mathbb {h}}}^n $在$ H $ -CONVEX函数中吞噬的属性。从Capogna和Maldonado引入的水平部分开始，我们考虑了一个新的概念，称为$ {\ Mathbb {h}}}^n $ - section，以及与$ {\ Mathbb {h}}}^n $ - $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h $ h $ chconve figinity fornication formince fornication formince new of gotulfing forkity的新条件。 $ {\ mathbb {h}}^n。$这些部分（作为水平部分合适的工会）在尺寸较大；事实上，$ {\ mathbb {h}}^n $ - sections及其吞噬属性将导致以$ {\ mathbb {h}}^n $在$ {\ mathbb {h Mathbb {h}}^n $中的定义，以类似于Aimar，Forzani，Forzani，Forzani和Euclidean的情况。 $ h $ convex函数的$ h $ sections的属性以及与吞噬属性的联系。
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, 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 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 the property of round $H$-sections for an $H$-convex function, and by its connection with the engulfing properties.
