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arXiv · 2201.12125

Lipschitz continuity of the Hausdorff dimension of self-affine sponges at Sierpinski sponges

Nuno Luzia
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Abstract

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.

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Nuno Luzia. 2022-01-28. Lipschitz continuity of the Hausdorff dimension of self-affine sponges at Sierpinski sponges. https://arxiv.org/abs/2201.12125

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