Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down

• Autorzy: Matthieu Joseph , Tapio Rajala
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Ahlfors-regularity; biLipschitz pieces; BPI-spaces

Kategorie tematyczne

• 26B05: Continuity and differentiation questions
• 28A80: Fractals

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 78-97

Daty

wydano

2017-11-27

otrzymano

2017-08-16

zaakceptowano

2017-10-24

online

2017-11-16

Twórcy

autor

Matthieu Joseph

• 07,

autor

Tapio Rajala

• ,

Identyfikatory

DOI

10.1515/agms-2017-0005