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arXiv · 1605.01287

Hausdorff dimension of weighted singular vectors

Lingmin Liao·Ronggang Shi·Omri N. Solan·Nattalie Tamam
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Abstract

Let $w=(w_1, w_2)$ be a pair of positive real numbers with $w_1+w_2=1$ and $w_1\ge w_2$. We show that the set of $w$-weighted singular vectors in $\mathbb R^2$ has Hausdorff dimension $2- \frac{1}{1+w_1}$. This extends the previous work of Yitwah Cheung on the Hausdorff dimension of the usual (unweighted) singular vectors in $\mathbb R^2$.

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Lingmin Liao, Ronggang Shi, Omri N. Solan, Nattalie Tamam. 2016-05-04. Hausdorff dimension of weighted singular vectors. https://arxiv.org/abs/1605.01287

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