拟对称极小的齐次完全集

肖映青

数学学报 ›› 2013, Vol. 56 ›› Issue (4) : 527-536.

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数学学报 ›› 2013, Vol. 56 ›› Issue (4) : 527-536. DOI: 10.12386/A2013sxxb0053
论文

拟对称极小的齐次完全集

    肖映青
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Quasisymmetrically Minimal Homogeneous Perfect Sets

    Ying Qing XIAO
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文章历史 +

摘要

本文用质量分布原理,证明了由有界正整数序列定义的Hausdorff维数为1的齐次完全集是一维拟对称极小的.

Abstract

In this paper, using the mass distribution principle, we show that the homogeneous perfect set of Hausdorff dimension 1, defined by a bounded sequence of positive integers is minimal for 1-dimensional quasisymmetric maps.

关键词

齐次完全集 / 拟对称映射 / 拟对称极小集

Key words

homogenous perfect set / quasisymmetric map / quasisymmetrically minimal set

引用本文

导出引用
肖映青. 拟对称极小的齐次完全集. 数学学报, 2013, 56(4): 527-536 https://doi.org/10.12386/A2013sxxb0053
Ying Qing XIAO. Quasisymmetrically Minimal Homogeneous Perfect Sets. Acta Mathematica Sinica, Chinese Series, 2013, 56(4): 527-536 https://doi.org/10.12386/A2013sxxb0053

参考文献

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[8] Wen Z. Y., Mathematical Foundations of Fractal Geometry, Shanghai Scientific and Technological Education Publishing House, Shanghai, 2000.

[9] Wen Z. Y., Wu J., Hausdorff dimension of homogeneous perfect sets, Acta Math. Hungar., 2005, 107: 35-44.

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基金

国家自然科学基金资助项目(11126194,11071059);湖南省自然科学基金资助项目(12JJB002);湖南大学中央高校专项基金资助项目(531107040317)

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