Pseudotangents to Lipschitz curves

Abstract

In this paper, we extend the result of arXiv:2409.13662 by showing that the set on which every pseudotangent is obtained on a Lipschitz curve can be any compact, uniformly disconnected set in Euclidean space which admits any Lipschitz capture. We do not obtain a characterization of such sets however, indeed we leave open the very strong question of whether or not a Lipschitz curve can obtain every pseudotangent at every point.