Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down

Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down

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...

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Main Authors: Joseph Matthieu, Rajala Tapio
Format: Article
Language:English
Published: De Gruyter 2017-11-01
Series:Analysis and Geometry in Metric Spaces
Subjects:
ahlfors-regularity
bilipschitz pieces
bpi-spaces
primary 26b05
secondary 28a80
Online Access:https://doi.org/10.1515/agms-2017-0005
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spelling doaj-25a5edb1ec40474599c23795bb8db4722021-09-06T19:39:45ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742017-11-0151789710.1515/agms-2017-0005agms-2017-0005Products of Snowflaked Euclidean Lines Are Not Minimal for Looking DownJoseph Matthieu0Rajala Tapio1Département de Mathématiques, École Normale Supérieure de Lyon, 69364 Lyon Cedex 07, FranceUniversity of Jyvaskyla, Department of Mathematics and Statistics, P.O. Box 35 (MaD), FI-40014 University of Jyvaskyla, Jyvaskyla, FinlandWe 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.https://doi.org/10.1515/agms-2017-0005ahlfors-regularitybilipschitz piecesbpi-spacesprimary 26b05secondary 28a80
collection DOAJ
language English
format Article
sources DOAJ
author Joseph Matthieu
Rajala Tapio
spellingShingle Joseph Matthieu
Rajala Tapio
Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
Analysis and Geometry in Metric Spaces
ahlfors-regularity
bilipschitz pieces
bpi-spaces
primary 26b05
secondary 28a80
author_facet Joseph Matthieu
Rajala Tapio
author_sort Joseph Matthieu
title Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
title_short Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
title_full Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
title_fullStr Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
title_full_unstemmed Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
title_sort products of snowflaked euclidean lines are not minimal for looking down
publisher De Gruyter
series Analysis and Geometry in Metric Spaces
issn 2299-3274
publishDate 2017-11-01
description 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.
topic ahlfors-regularity
bilipschitz pieces
bpi-spaces
primary 26b05
secondary 28a80
url https://doi.org/10.1515/agms-2017-0005
work_keys_str_mv AT josephmatthieu productsofsnowflakedeuclideanlinesarenotminimalforlookingdown
AT rajalatapio productsofsnowflakedeuclideanlinesarenotminimalforlookingdown
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