论文标题
Heisenberg Group $ \ Mathbb {H}^n $中的河流电流和电流切片
Sub-Riemannian Currents and Slicing of Currents in the Heisenberg group $\mathbb{H}^n$
论文作者
论文摘要
本文旨在定义和研究Heisenberg Group $ \ Mathbb {H}^n $中的电流和片段。电流根据其集成属性和边界的集成属性，可以分类为子空间，并假设它们的支持是紧凑的，我们可以使用有限质量的电流来定义海森堡电流的切片概念并为其显示一些重要的特性。尽管在Riemannian设置中，某些此类属性同样是正确的，但另一些属性则带来深层后果，因为它们不包括中间维度的切片$ n $，这为开发紧凑定理的可能性打开了新的挑战和场景。此外，这表明对第一个海森伯格集团的流量研究$ \ mathbb {h}^1 $与其他情况有所不同，因为这是唯一的情况下，高空的尺寸为$ 2n-1 $，与中间维度$ n $重合的$ 2N-1 $，这触发了相关的脉络脉络脉络脉络脉络脉络脉络脉络脉络的复合物。
This paper aims to define and study currents and slices of currents in the Heisenberg group $\mathbb{H}^n$. Currents, depending on their integration properties and on those of their boundaries, can be classified into subspaces and, assuming their support to be compact, we can work with currents of finite mass, define the notion of slices of Heisenberg currents and show some important properties for them. While some such properties are similarly true in Riemannian settings, others carry deep consequences because they do not include the slices of the middle dimension $n$, which opens new challenges and scenarios for the possibility of developing a compactness theorem. Furthermore, this suggests that the study of currents on the first Heisenberg group $\mathbb{H}^1$ diverges from the other cases, because that is the only situation in which the dimension of the slice of a hypersurface, $2n-1$, coincides with the middle dimension $n$, which triggers a change in the associated differential operator in the Rumin complex.
