雪花欧氏线的产品不是最小的向下看

Pub Date : 2017-08-09 DOI:10.1515/agms-2017-0005

Matthieu Joseph, T. Rajala

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引用次数: 0

摘要

摘要本文证明了雪花欧几里得线的积在向下看时不是极小的。这个问题是大卫和塞姆斯在《破碎的分形与破碎的梦》第11.17题中提出的。这个证明使用了Le Donne, Li和Rajala提出的论据来证明海森堡群在向下看时不是最小的。通过一种捷径的方法，我们定义了一个新的距离d，使得雪花欧几里得线的乘积俯视(RN, d)，而不是相反。

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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Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down

Abstract We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance d such that the product of snowflaked Euclidean lines looks down on (RN , d), but not vice versa.

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