Year: 2026
Type: preprint
Abstract: We prove optimal dual Furstenberg estimates for Frostman and Katz--Tao configurations for which the shadings are not locally concentrated near pencils. The starting point is the sticky estimate of Orponen and Shmerkin in a companion paper. We deduce restricted projection theorems in the plane and in higher dimensions. In particular, Ahlfors-regular measures on the circle satisfy a Marstrand-type projection theorem. Applications include restricted projections to surfaces in the $\mathbb{G}(4,2)$ Grassmannian, pinned distances, discretized sum-product, and a new proof of the dimension formula for planar self-affine sets.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221532277