6533b872fe1ef96bd12d3856

RESEARCH PRODUCT

Removable sets for intrinsic metric and for holomorphic functions

Leonid V. KovalevSergei KalmykovTapio Rajala

subject

Pure mathematicsintrinsic metricsGeneral MathematicsHolomorphic function01 natural sciencesIntrinsic metricSet (abstract data type)Mathematics - Metric GeometryTotally disconnected spaceholomorphic functionsFOS: MathematicsHausdorff measure0101 mathematicsComplex Variables (math.CV)MathematicsPartial differential equationmatematiikkaMathematics - Complex Variables010102 general mathematicsMetric Geometry (math.MG)Codimensionmetriset avaruudet010101 applied mathematicsMetric space28A78 (Primary) 26A16 30C62 30H05 49Q15 51F99 (Secondary)Analysis

description

We study 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 set with finite Hausdorff measure of codimension 1 is metrically removable, which answers 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.

yearjournalcountryeditionlanguage
2019-10-01
https://dx.doi.org/10.48550/arxiv.1707.07363