Curvature densities of self-similar sets

Details Curvature densities of self-similar sets Curvature densities of self-similar sets

2010-09-30

arxiv.org/abs/1009.6162v1

Mathematics

Metric Geometry

17 pages

Scientific paper

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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