Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down

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...

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Autores principales:	Joseph Matthieu, Rajala Tapio
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2017
Materias:	ahlfors-regularity bilipschitz pieces bpi-spaces primary 26b05 secondary 28a80 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/25a5edb1ec40474599c23795bb8db472
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id	oai:doaj.org-article:25a5edb1ec40474599c23795bb8db472
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spelling	oai:doaj.org-article:25a5edb1ec40474599c23795bb8db4722021-12-05T14:10:38ZProducts of Snowflaked Euclidean Lines Are Not Minimal for Looking Down2299-327410.1515/agms-2017-0005https://doaj.org/article/25a5edb1ec40474599c23795bb8db4722017-11-01T00:00:00Zhttps://doi.org/10.1515/agms-2017-0005https://doaj.org/toc/2299-3274We 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.Joseph MatthieuRajala TapioDe Gruyterarticleahlfors-regularitybilipschitz piecesbpi-spacesprimary 26b05secondary 28a80AnalysisQA299.6-433ENAnalysis and Geometry in Metric Spaces, Vol 5, Iss 1, Pp 78-97 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	ahlfors-regularity bilipschitz pieces bpi-spaces primary 26b05 secondary 28a80 Analysis QA299.6-433
spellingShingle	ahlfors-regularity bilipschitz pieces bpi-spaces primary 26b05 secondary 28a80 Analysis QA299.6-433 Joseph Matthieu Rajala Tapio Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
description	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.
format	article
author	Joseph Matthieu Rajala Tapio
author_facet	Joseph Matthieu Rajala Tapio
author_sort	Joseph Matthieu
title	Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
title_short	Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
title_full	Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
title_fullStr	Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
title_full_unstemmed	Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down
title_sort	products of snowflaked euclidean lines are not minimal for looking down
publisher	De Gruyter
publishDate	2017
url	https://doaj.org/article/25a5edb1ec40474599c23795bb8db472
work_keys_str_mv	AT josephmatthieu productsofsnowflakedeuclideanlinesarenotminimalforlookingdown AT rajalatapio productsofsnowflakedeuclideanlinesarenotminimalforlookingdown
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Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down

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