海森堡群中右协集投影引起的维度畸变

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-02-12 DOI:10.4171/JFG/106

Terence L. J. Harris, Chi N. Y. Huynh, Fernando Roman-Garcia

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引用次数: 4

摘要

我们研究了Heisenberg群中纤维是水平面的右陪集的垂直投影族$\mathbb｛H｝^n$。我们证明了这些映射下集合的Hausdorff维数失真的下界，关于欧几里得度量和自然商度量。我们证明了这些边界在可能维度范围的很大一部分是尖锐的，并给出了该范围剩余部分的推测尖锐下界。我们的结果还使我们改进了$\mathbb｛H｝^n$中标准垂直投影族的已知几乎确定的下界。

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Dimension distortion by right coset projections in the Heisenberg group

We study the family of vertical projections whose fibers are right cosets of horizontal planes in the Heisenberg group, $\mathbb{H}^n$. We prove lower bounds for Hausdorff dimension distortion of sets under these mappings, with respect to the Euclidean metric and also the natural quotient metric. We show these bounds are sharp in a large part of the range of possible dimension, and give conjectured sharp lower bounds for the remaining part of the range. Our result also lets us improve the known almost sure lower bound for the standard family of vertical projections in $\mathbb{H}^n$.

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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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.