Large Slices Through Self Affine Carpets

Amir Algom; Meng Wu

doi:10.1007/978-3-031-80453-3_1

Large Slices Through Self Affine Carpets

Amir Algom
, Meng Wu

Department of Mathematics, Physics and Computer Science (Oranim Campus)

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Let F⊆[0,1]² be a Bedford-McMullen carpet defined by exponents m>n, that projects to [0, 1] on the y-axis. We show that under mild conditions on F, there are many non principle lines ℓ such that dim^∗F∩ℓ=dim^∗F-1, where dim^∗ is Furstenberg’s star dimension (maximal dimension of a microset). This exhibits the sharpness of recent Furstenberg-type slicing theorems obtained by Algom (2020) about upper bounds on the dimension of every such slice.

Original language	English
Title of host publication	Trends in Mathematics
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	1-16
Number of pages	16
DOIs	https://doi.org/10.1007/978-3-031-80453-3_1
State	Published - 2025

Publication series

Name	Trends in Mathematics
Volume	Part F319
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-031-80453-3_1

Cite this

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abstract = "Let F⊆[0,1]2 be a Bedford-McMullen carpet defined by exponents m>n, that projects to [0, 1] on the y-axis. We show that under mild conditions on F, there are many non principle lines ℓ such that dim∗F∩ℓ=dim∗F-1, where dim∗ is Furstenberg{\textquoteright}s star dimension (maximal dimension of a microset). This exhibits the sharpness of recent Furstenberg-type slicing theorems obtained by Algom (2020) about upper bounds on the dimension of every such slice.",

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AB - Let F⊆[0,1]2 be a Bedford-McMullen carpet defined by exponents m>n, that projects to [0, 1] on the y-axis. We show that under mild conditions on F, there are many non principle lines ℓ such that dim∗F∩ℓ=dim∗F-1, where dim∗ is Furstenberg’s star dimension (maximal dimension of a microset). This exhibits the sharpness of recent Furstenberg-type slicing theorems obtained by Algom (2020) about upper bounds on the dimension of every such slice.

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M3 - Chapter

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BT - Trends in Mathematics

PB - Springer Science and Business Media Deutschland GmbH

ER -

Large Slices Through Self Affine Carpets

Abstract

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