Products of snowflaked Euclidean lines are not minimal for looking down
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
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Analysis and Geometry in Metric SpacesDate
2017Copyright
© 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.
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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Related funder(s)
Academy of FinlandFunding program(s)
Research post as 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.License
Except where otherwise noted, this item's license is described as © 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.