Year: 2026
Type: preprint
Abstract: We prove the hyperplane winning property of weighted badly approximable vectors inside nondegenerate analytic manifolds and affine subspaces satisfying almost optimal Diophantine conditions. This, in particular, answers a conjecture of Badziahin--Velani for higher-dimensional manifolds, including affine cases that were understood only in $\mathbb{R}^2$.
Source: arXiv (Cornell University)
Authors: Datta, Shreyasi, Shao, Liyang
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221079263