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
Published inAnalysis and Geometry in Metric Spaces
© 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.
PublisherDe Gruyter Open
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Related funder(s)Academy of Finland
Funding program(s)Research post as Academy Research Fellow, AoF
Additional information about fundingM.J. is supported by Erasmus and ExploRA’Sup grants. T.R. is supported by the Academy of Finland project no. 274372.
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.
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