6533b827fe1ef96bd1286fea
RESEARCH PRODUCT
Products of snowflaked Euclidean lines are not minimal for looking down
Matthieu JosephTapio Rajalasubject
Ahlfors-regularity26B05 (Primary) 28A80 (Secondary)01 natural sciences010104 statistics & probabilityFractalMathematics - Metric GeometryEuclidean geometryClassical Analysis and ODEs (math.CA)FOS: MathematicsHeisenberg groupMathematics::Metric GeometryBPI-spacesbpi-spacessecondary 28a800101 mathematicsbilipschitz piecesMathematicsDiscrete mathematicsQA299.6-433ahlfors-regularityApplied Mathematics010102 general mathematicsprimary 26b05Metric Geometry (math.MG)biLipschitz piecesMathematics - Classical Analysis and ODEsProduct (mathematics)Geometry and TopologyAnalysisdescription
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 $(\mathbb R^N,d)$, but not vice versa.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-08-09 |