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math.CA2026
On the Peres--Schlag orthogonal projection problem and Kakeya-type sets
Guo-Dong Hong, Chong-Wei Liang, Chun-Yen Shen
We investigate the Peres--Schlag nonempty interior problem for orthogonal projections in both the finite-field and Euclidean settings. Over finite fields , we employ…
math.CA2024
A study guide for "On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" after T. Orponen and P. Shmerkin
Jacob B. Fiedler, Guo-Dong Hong, Donggeun Ryou +1
This article is a study guide for ``On the Hausdorff dimension of Furstenberg sets and orthogonal projections in the plane" by Orponen and Shmerkin. We begin by introducing Fursten…
math.CA2021
The Group Action Method and Radial Projection
Guo-Dong Hong, Chun-Yen Shen
The group action methods have been playing an important role in recent studies about the configuration problems inside a compact set in Euclidean spaces with given Hausdorff di…