Furstenberg-type estimates under mild non-concentration assumptions

TL;DR

This paper establishes precise discretized estimates related to Furstenberg sets under relaxed non-concentration conditions, advancing understanding in geometric measure theory.

Contribution

It introduces sharper discretized bounds for Furstenberg-type problems under milder non-concentration assumptions than prior research.

Findings

Proved sharp δ-discretized estimates for Furstenberg sets

Extended results to weaker non-concentration conditions

Improved bounds compared to previous works

Abstract

We prove sharp $\delta$-discretised versions of some variants of the Furstenberg set problem under weaker or different non-concentration assumptions compared to previous works.