Improved Versions of Some Furstenberg Type Slicing Theorems for Self-Affine Carpets

Amir Algom; Meng Wu

doi:10.1093/imrn/rnab318

Improved Versions of Some Furstenberg Type Slicing Theorems for Self-Affine Carpets

Amir Algom
, Meng Wu

Research output: Contribution to journal › Article › peer-review

Abstract

Let F be a Bedford-McMullen carpet defined by independent integer exponents. We prove that for every line ℓ ⊆ ℝ² not parallel to the major axes, (Equation presented) and (Equation presented) where dim^∗ is Furstenberg's star dimension (maximal dimension of microsets). This improves the state-of-the-art results on Furstenberg type slicing Theorems for affine invariant carpets.

Original language	English
Pages (from-to)	2304-2343
Number of pages	40
Journal	International Mathematics Research Notices
Volume	2023
Issue number	3
DOIs	https://doi.org/10.1093/imrn/rnab318
State	Published - 1 Feb 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The Author(s) 2021. Published by Oxford University Press. All rights reserved.

ASJC Scopus subject areas

General Mathematics

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10.1093/imrn/rnab318

Cite this

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abstract = "Let F be a Bedford-McMullen carpet defined by independent integer exponents. We prove that for every line ℓ ⊆ ℝ2 not parallel to the major axes, (Equation presented) and (Equation presented) where dim∗ is Furstenberg's star dimension (maximal dimension of microsets). This improves the state-of-the-art results on Furstenberg type slicing Theorems for affine invariant carpets.",

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N2 - Let F be a Bedford-McMullen carpet defined by independent integer exponents. We prove that for every line ℓ ⊆ ℝ2 not parallel to the major axes, (Equation presented) and (Equation presented) where dim∗ is Furstenberg's star dimension (maximal dimension of microsets). This improves the state-of-the-art results on Furstenberg type slicing Theorems for affine invariant carpets.

AB - Let F be a Bedford-McMullen carpet defined by independent integer exponents. We prove that for every line ℓ ⊆ ℝ2 not parallel to the major axes, (Equation presented) and (Equation presented) where dim∗ is Furstenberg's star dimension (maximal dimension of microsets). This improves the state-of-the-art results on Furstenberg type slicing Theorems for affine invariant carpets.

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Improved Versions of Some Furstenberg Type Slicing Theorems for Self-Affine Carpets

Abstract

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