Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down

Matthieu Joseph, and Tapio Rajala. "Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down." Analysis and Geometry in Metric Spaces 5.1 (2017): 78-97. <http://eudml.org/doc/288370>.

@article{MatthieuJoseph2017,
abstract = {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.},
author = {Matthieu Joseph, Tapio Rajala},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Ahlfors-regularity; biLipschitz pieces; BPI-spaces},
language = {eng},
number = {1},
pages = {78-97},
title = {Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down},
url = {http://eudml.org/doc/288370},
volume = {5},
year = {2017},
}

TY - JOUR
AU - Matthieu Joseph
AU - Tapio Rajala
TI - Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
JO - Analysis and Geometry in Metric Spaces
PY - 2017
VL - 5
IS - 1
SP - 78
EP - 97
AB - 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.
LA - eng
KW - Ahlfors-regularity; biLipschitz pieces; BPI-spaces
UR - http://eudml.org/doc/288370
ER -