Curvature bounds for neighborhoods of self-similar sets
In some recent work, fractal curvatures and fractal curvature measures , , have been determined for all self-similar sets in , for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent formulations...