Removable sets for intrinsic metric

We discuss the subsets of metric spaces that are negligible for the infimal length of connecting curves, such sets are called metrically removable. In particular, we show that every totally disconnected planar set of finite length is metrically removable, which answers the two-dimensional case of a question raised by Hakobyan and Herron. Based on joint research with L.V. Kovalev and T. Rajala.