Marstrand–Mattila rectifiability criterion for 1-codimensional measures in Carnot groups

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-15 DOI:10.2140/apde.2023.16.927

Andrea Merlo

引用次数: 6

Abstract

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.

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Carnot群中一维测度的Marstrand-Mattila可整流判据

本文证明了卡诺群中$1$-余维测度的切线的平坦性蕴涵了$C^1_\mathbb{G}$-可纠偏性。作为应用，我们证明了Heisenberg群中$(2n+1)$-密度的测度$\mathbb{H}^n$是$C^1_{\mathbb{H}^n}$-可纠偏的，给出了Preiss可纠偏定理的第一个非欧几里德推广，并给出了一般卡诺群中有限周长集的内征Lipschitz可纠偏的判据。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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