Hausdorff dimension of weighted singular vectors in R2\mathbb R^2

  • Lingmin Liao

    Université Paris-Est Créteil, France
  • Ronggang Shi

    Fudan University, China
  • Omri N. Solan

    Tel Aviv University, Israel
  • Nattalie Tamam

    Tel Aviv University, Israel
Hausdorff dimension of weighted singular vectors in $\mathbb R^2$ cover
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Abstract

Let w=(w1,w2)w=(w_1, w_2) be a pair of positive real numbers with w1+w2=1w_1+w_2=1 and w1w2w_1\ge w_2. We show that the set of ww-weighted singular vectors in R2\mathbb R^2 has Hausdorff dimension 211+w12- \frac{1}{1+w_1}. This extends the previous work of Yitwah Cheung on the Hausdorff dimension of the usual (unweighted) singular vectors in R2\mathbb R^2.

Cite this article

Lingmin Liao, Ronggang Shi, Omri N. Solan, Nattalie Tamam, Hausdorff dimension of weighted singular vectors in R2\mathbb R^2. J. Eur. Math. Soc. 22 (2020), no. 3, pp. 833–875

DOI 10.4171/JEMS/934