Search results for "secondary 28a80"

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Products of snowflaked Euclidean lines are not minimal for looking down

2017

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.

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 TopologyAnalysis
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Random cutout sets with spatially inhomogeneous intensities

2015

We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal spaces using the multifractal decomposition of the average densities for the natural measures.

General MathematicsStructure (category theory)Hausdorff dimensionDynamical Systems (math.DS)01 natural sciencesMeasure (mathematics)010104 statistics & probabilityCorollaryDimension (vector space)Classical Analysis and ODEs (math.CA)FOS: MathematicsMathematics::Metric Geometry0101 mathematicsMathematics - Dynamical SystemsMathematicsmatematiikkaHausdorffin dimensioProbability (math.PR)010102 general mathematicsMathematical analysisMultifractal systemPoissonian CutoutMetric spaceMathematics - Classical Analysis and ODEsHausdorff dimensionPrimary 60D05 Secondary 28A80 37D35 37C45Intensity (heat transfer)Mathematics - Probability
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