论文标题
本质上是Lipschitz的部分和对公制组的应用
Intrinsically Lipschitz sections and applications to metric groups
论文作者
论文摘要
我们在公制空间的背景下介绍了本质上lipschitz图的概念。这是Franchi，Serapioni和Serra Cassano所考虑的Carnot群体中的广泛概括，后来又被许多其他人所考虑的。我们通过将注意力集中在图形上作为公制空间的亚集的图像来进行，由商图的图像给出，我们需要本质上的Lipschitz条件。我们将对拓扑产品没有任何功能，而不是我们在商图基础上考虑一个指标。我们的结果是：Ascoli-arzelà紧凑型定理，AHLFORS的定理和某些延伸定理，用于部分定义的本质上lipschitz部分。 Franchi，Serapioni和Serra Cassano以及Vittone的已知结果将是我们的推论。
We introduce a notion of intrinsically Lipschitz graphs in the context of metric spaces. This is a broad generalization of what in Carnot groups has been considered by Franchi, Serapioni, and Serra Cassano, and later by many others. We proceed by focusing our attention on the graphs as subsets of a metric space given by the image of a section of a quotient map and we require an intrinsically Lipschitz condition. We shall not have any function on a topological product, not we shall consider a metric on the base of the quotient map. Our results are: an Ascoli-Arzelà compactness theorem, an Ahlfors regularity theorem, and some extension theorems for partially defined intrinsically Lipschitz sections. Known results by Franchi, Serapioni, and Serra Cassano, and by Vittone will be our corollaries.
