论文标题
固有的Lipschitz部分，无线性商地图
Intrinsic Lipschitz sections of no-linear quotient maps
论文作者
论文摘要
Le Donne和作者在公制空间的背景下介绍了固定商地图$π$的所谓本质上的Lipschitz部分。此外，当商映射也是线性时，作者介绍了内在的Cheeger Energy的概念。在本说明中，我们调查了$π$的非线性性。特别是，当$π$满足较弱的情况时，我们发现了固有斜率的莱布尼兹公式。之后，我们将注意力集中在Carnot群体上，并使用固有扩张的特性，我们表明Lipschitz部分的扩张也是如此。最后，在步骤2的Carnot组中，我们提供了适当的额外条件，以便获得两个本质上Lipschitz部分的总和。
Le Donne and the author introduced the so-called intrinsically Lipschitz sections of a fixed quotient map $π$ in the context of metric spaces. Moreover, the author introduced the concept of intrinsic Cheeger energy when the quotient map is also linear. In this note we investigate about the non linearity of $π$. In particular, we find a Leibniz formula for the intrinsic slope when $π$ satisfies a weaker condition. After that, we focus our attention on Carnot groups and using the properties of intrinsic dilations we show that the dilation of a Lipschitz section is so too. Finally, in Carnot groups of step 2, we give a suitable additional condition in order to get the sum of two intrinsically Lipschitz sections is so too.
