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arXiv · 1009.6162

Curvature densities of self-similar sets

Jan Rataj·Martina Zähle
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Abstract

For a large class of self-similar sets F in R^d analogues of the higher order mean curvatures of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature. They are shown to be the densities of associated fractal curvature measures, which are all multiples of the corresponding Hausdorff measures on F, due to its self-similarity. This local approach based on ergodic theory for an associated dynamical system enables us to extend former global curvature results.

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Jan Rataj, Martina Zähle. 2010-09-30. Curvature densities of self-similar sets. https://arxiv.org/abs/1009.6162

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