A dichotomy of sets via typical differentiability

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

External organisations

  • Department of Mathematics, University of Innsbruck

Abstract

We obtain a criterion for an analytic subset of a Euclidean space to contain points of differentiability of a typical Lipschitz function, namely, that it cannot be covered by countably many sets, each of which is closed and purely unrectifiable (has zero length intersection with every $C^1$ curve). Surprisingly, we establish that any set failing this criterion witnesses the opposite extreme of typical behaviour: In any such coverable set a typical Lipschitz function is everywhere severely non-differentiable.

Details

Original languageEnglish
Number of pages56
JournalForum of Mathematics, Sigma
Publication statusAccepted/In press - 27 May 2020