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Products of snowflaked Euclidean lines are not minimal for looking down

Abstract
We show that products of snow aked 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 de ne a new distance d such that the product of snow aked Euclidean lines looks down on (R N , d), but not vice versa.
Main Authors
Joseph, Matthieu Rajala, Tapio
Format
Articles Research article
Published
2017
Series
Analysis and Geometry in Metric Spaces
Subjects
Ahlfors-regularity
biLipschitz pieces
BPI-spaces
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/27368745
Publisher
De Gruyter Open
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201711204299Use this for linking
Review status
Peer reviewed
ISSN
2299-3274
DOI
https://doi.org/10.1515/agms-2017-0005
Language
English
Published in
Analysis and Geometry in Metric Spaces
Citation
  • Joseph, M., & Rajala, T. (2017). Products of snowflaked Euclidean lines are not minimal for looking down. Analysis and Geometry in Metric Spaces, 5(1), 78-97. https://doi.org/10.1515/agms-2017-0005
License
Open Access
Funder(s)
Research Council of Finland
Funding program(s)
Akatemiatutkija, SA
Academy Research Fellow, AoF
Research Council of Finland
Additional information about funding
M.J. is supported by Erasmus and ExploRA’Sup grants. T.R. is supported by the Academy of Finland project no. 274372.
Copyright© 2017 Matthieu Joseph and Tapio Rajala, published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-Non-Commercial-NoDerivs 4.0 License.

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description We show that products of snow aked 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 de ne a new distance d such that the product of snow aked Euclidean lines looks down on (R N , d), but not vice versa.
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spellingShingle Products of snowflaked Euclidean lines are not minimal for looking down Joseph, Matthieu Rajala, Tapio Ahlfors-regularity biLipschitz pieces BPI-spaces Analysis and Geometry in Metric Spaces
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title 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_short Products of snowflaked Euclidean lines are not minimal for looking down
title_sort Products of snowflaked Euclidean lines are not minimal for looking down
topic Ahlfors-regularity biLipschitz pieces BPI-spaces
yso_count_txtF 0

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