Curvature densities of self-similar sets Jan RatajMartina Zahle 28A8028A7528A7837A49Q1553C65self-similar setsfractal curvaturesdynamical system For a large class of self-similar sets $F$ in $\mathbb{R}^d$, 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 total curvature results. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4681 10.1512/iumj.2012.61.4681 en Indiana Univ. Math. J. 61 (2012) 1425 - 1449 state-of-the-art mathematics http://iumj.org/access/