论文标题
Lipschitz在Sierpinski海绵的Hausdorff尺寸的Hausdorff尺寸
Lipschitz continuity of the Hausdorff dimension of self-affine sponges at Sierpinski sponges
论文作者
论文摘要
如今，众所周知的结果是，Sierpinski地毯[4]和[20]的Hausdorff维度[4]和[20]以及对Lalley-Gatzouras地毯的概括是众所周知的结果，是通过尺寸的变异原理获得的公式。我们分别称这些地毯sierpinski海绵和自动伴随海绵的多维版本。在本文中，我们表明，在R3中定义的自伴海海绵的Hausdorff尺寸是Sierpinski海绵的Lipschitz连续功能。
The Hausdorff dimension of general Sierpinski carpets, [4] and [20], and the generalization on Lalley-Gatzouras carpets, [10], are today well known results, the formulas being obtain via the variational principle for the dimension. We call the multidimensional versions of these carpets Sierpinski sponges and self-affine sponges, respectively,. In this paper we show that the Hausdorff dimension of self-affine sponges, defined in R3, is a Lipschitz continuous function at Sierpinski sponges.
