Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2017-08-09 DOI:10.1515/agms-2017-0005

Matthieu Joseph, T. Rajala

引用次数: 0

Abstract

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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雪花欧氏线的产品不是最小的向下看

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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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.