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Hyperplane winning for bad in manifolds
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 ℝ2.
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BibTeX
@misc{datta2026hyperplane,
title = {{Hyperplane winning for bad in manifolds}},
author = {Shreyasi Datta and Liyang Shao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12037},
eprint = {2610.12037},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12037},
}
RIS
TY - UNPB
TI - Hyperplane winning for bad in manifolds
AU - Shreyasi Datta
AU - Liyang Shao
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12037
UR - https://arxiv.org/abs/2610.12037
AB - 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 ℝ^2.
ER -