Cover Image

Dimensions of Furstenberg sets and an extension of Bourgain's projection theorem

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Shmerkin, Pablo, Wang, Hong
Format:	Preprint
Published:	2022
Subjects:	Classical Analysis and ODEs Combinatorics Metric Geometry 28A80 (Primary) 28A75, 28A78 (Secondary)
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane
by: Orponen, Tuomas, et al.
Published: (2021)

On the packing dimension of Furstenberg sets
by: Shmerkin, Pablo
Published: (2020)

On the distance sets spanned by sets of dimension $d/2$ in $\mathbb{R}^d$
by: Shmerkin, Pablo, et al.
Published: (2021)

A study guide for "On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" after T. Orponen and P. Shmerkin
by: Fiedler, Jacob B., et al.
Published: (2024)

Projections, Furstenberg sets, and the $ABC$ sum-product problem
by: Orponen, Tuomas, et al.
Published: (2023)

Furstenberg sets estimate in the plane
by: Ren, Kevin, et al.
Published: (2023)

A nonlinear version of Bourgain's projection theorem
by: Shmerkin, Pablo
Published: (2020)

On variants of the Furstenberg set problem
by: Fraser, Jonathan M.
Published: (2024)

Slices and distances: on two problems of Furstenberg and Falconer
by: Shmerkin, Pablo
Published: (2021)

Simple proofs of discretised projection theorems
by: O'Regan, William, et al.
Published: (2025)

On the Hausdorff dimension of circular Furstenberg sets
by: Fässler, Katrin, et al.
Published: (2023)

Kaufman and Falconer estimates for radial projections and a continuum version of Beck's Theorem
by: Orponen, Tuomas, et al.
Published: (2022)

Self-similar sets and Lipschitz graphs
by: Davey, Blair, et al.
Published: (2024)

Furstenberg-type estimates under mild non-concentration assumptions
by: Orponen, Tuomas, et al.
Published: (2026)

Exceptional sets for length under restricted families of projections onto lines in $\mathbb{R}^3$
by: Harris, Terence L. J.
Published: (2024)

Spread Furstenberg Sets
by: Bright, Paige, et al.
Published: (2024)

Generalised lower Assouad-type dimensions and their interpolations
by: Chen, Haipeng, et al.
Published: (2026)

Self-embedding similitudes of Bedford-McMullen carpets with dependent ratios
by: Xiao, Jian-Ci
Published: (2024)

New improvement to Falconer distance set problem in higher dimensions
by: Du, Xiumin, et al.
Published: (2023)

An improved bound for the dimension of $(α,2α)$-Furstenberg sets
by: Héra, Kornélia, et al.
Published: (2020)

Discretised sum-product theorems by Shannon-type inequalities
by: Máthé, András, et al.
Published: (2023)

Full measure universality for Cantor Sets
by: Shmerkin, Pablo, et al.
Published: (2025)

Radial Projections in $\mathbb{R}^n$ Revisited
by: Bright, Paige, et al.
Published: (2024)

A Continuum Erdős-Beck Theorem
by: Bright, Paige, et al.
Published: (2024)

Packing dimension of vertical projections in the Heisenberg group
by: Harris, Terence L. J.
Published: (2024)

Sharp Favard length of random Cantor sets
by: Chang, Alan, et al.
Published: (2025)

Structure of sets with nearly maximal Favard length
by: Chang, Alan, et al.
Published: (2022)

Analytic capacity and dimension of sets with plenty of big projections
by: Dąbrowski, Damian, et al.
Published: (2022)

An invitation to dimension interpolation
by: Fraser, Jonathan M.
Published: (2026)

From Lipschitz embedding to Lipschitz equivalence between dust-like self-similar sets
by: Ruan, Huo-Jun, et al.
Published: (2025)

On the volumes of simplices determined by a subset of $\mathbb{R}^d$
by: Shmerkin, Pablo, et al.
Published: (2023)

Pinned Dot Product Set Estimates
by: Bright, Paige, et al.
Published: (2024)

Minkowski dimension for measures
by: Falconer, Kenneth J., et al.
Published: (2020)

Sum-product phenomena for Ahlfors-regular sets
by: O'Regan, William
Published: (2025)

A Study Guide to "Kaufman and Falconer estimates for radial projections"
by: Bright, Paige, et al.
Published: (2024)

Applications of dimension interpolation to orthogonal projections
by: Fraser, Jonathan M.
Published: (2025)

Incidence bounds related to circular Furstenberg sets
by: Green, John, et al.
Published: (2025)

A Fourier analytic approach to exceptional set estimates for orthogonal projections
by: Fraser, Jonathan M., et al.
Published: (2024)

Weak Carleson conditions in uniformly rectifiable metric spaces: the WCD and alpha numbers
by: Krandel, Jared
Published: (2024)

A nonlinear projection theorem for Assouad dimension and applications
by: Fraser, Jonathan M.
Published: (2020)