Sergei Kalmykov (FEFU): Removable sets on the complex plane

SZTE, TTIK, Bolyai Intézet, Potenciálelmélet szeminárium

Abstract. We consider 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. The metrically removable sets are shown to be related to other classes of "thin" sets that appeared in the literature. They are also related to the removability problems for classes of holomorphic functions with restrictions on the derivative. (Based on joint research with L.V. Kovalev and T. Rajala).