论文标题
Marstrand-Mattila可重新讨论性标准，以$ 1 $ - 二维措施的carnot组
Marstrand-Mattila rectifiability criterion for $1$-codimensional measures in Carnot Groups
论文作者
论文摘要
本文专门表明，Carnot组中的$ 1 $编码措施的切线的平坦度暗示$ C^1_ \ Mathbb {G} $ - 可重新可相关性。 As applications we prove that measures with $(2n+1)$-density in the Heisenberg groups $\mathbb{H}^n$ are $C^1_{\mathbb{H}^n}$-rectifiable, providing the first non-Euclidean extension of Preiss's rectifiability theorem and a criterion for intrinsic Lipschitz rectifiability of finite一般Carnot组中的周长组。
This paper is devoted to show that the flatness of tangents of $1$-codimensional measures in Carnot Groups implies $C^1_\mathbb{G}$-rectifiability. As applications we prove that measures with $(2n+1)$-density in the Heisenberg groups $\mathbb{H}^n$ are $C^1_{\mathbb{H}^n}$-rectifiable, providing the first non-Euclidean extension of Preiss's rectifiability theorem and a criterion for intrinsic Lipschitz rectifiability of finite perimeter sets in general Carnot groups.
