论文标题
里克曼地毯和内在的bilipschitz图
Rickman rugs and intrinsic bilipschitz graphs
论文作者
论文摘要
本文研究了bilipschitz地图$ f \ colon \ mathbb {w} \ to \ mathbb {h} $的几何形状，其中$ \ mathbb {h} $是第一个heisenberg group，$ \ mathbb {w} \ subset \ subset \ subset \ subbb {此类地图的图像$ f（\ mathbb {w}）$在海森伯格集团中称为里克曼地毯。 主要定理指出，海森伯格集团中的里克曼地毯承认了固有的比利普斯奇图的电晕分解。作为推论，里克曼地毯可以通过固有的bilipschitz图来统一。在这里，固有的bilipschitz图是一张内在的Lipschitz图，同时也是Rickman地毯。一般的固有的Lipschitz图形不必以Bigolin和Vittone的例子为Rickman地毯，甚至是本地地毯。
This paper studies the geometry of bilipschitz maps $f \colon \mathbb{W} \to \mathbb{H}$, where $\mathbb{H}$ is the first Heisenberg group, and $\mathbb{W} \subset \mathbb{H}$ is a vertical subgroup of co-dimension $1$. The images $f(\mathbb{W})$ of such maps are called Rickman rugs in the Heisenberg group. The main theorem states that a Rickman rug in the Heisenberg group admits a corona decomposition by intrinsic bilipschitz graphs. As a corollary, Rickman rugs are countably rectifiable by intrinsic bilipschitz graphs. Here, an intrinsic bilipschitz graph is an intrinsic Lipschitz graph, which is simultaneously a Rickman rug. General intrinsic Lipschitz graphs need not be Rickman rugs, even locally, by an example of Bigolin and Vittone.
