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
Format
Articles
Research article
Published
2017
Series
Subjects
Publication in research information system
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
Funder(s)
Research Council of Finland
Funding program(s)
Akatemiatutkija, SA
Academy Research Fellow, AoF
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.