# Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down

Analysis and Geometry in Metric Spaces (2017)

- Volume: 5, Issue: 1, page 78-97
- ISSN: 2299-3274

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topMatthieu 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 -

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