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.
@article{bwmeta1.element.doi-10_1515_agms-2017-0005,
author = {Matthieu Joseph and Tapio Rajala},
title = {Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down},
journal = {Analysis and Geometry in Metric Spaces},
volume = {5},
year = {2017},
pages = {78-97},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2017-0005}
}
Matthieu Joseph; Tapio Rajala. Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down. Analysis and Geometry in Metric Spaces, Tome 5 (2017) pp. 78-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2017-0005/