This analysis computes Hausdorff dimension in the context of nondegenerate nonplanar curves, confirming a conjecture.
We compute the Hausdorff dimension of the set of simultaneously λ-well approximable points on the Veronese curve in R³ for 1/3 λ 3/5. This range for λ was predicted in the conjecture of Beresnevich and Yang from [3]. To the best of the author’s knowledge, this makes V₃ the first nondegenerate, nonplanar curve to confirm the lower bound part of this conjecture.
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Dmitry Badziahin (2026) studied this question.
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