Universal singular sets and unrectifiability

Richard Gratwick*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The geometry of universal singular sets has recently been studied by M. Csörnyei et al. [Arch. Ration. Mech. Anal. 190 (2008)(3), 371-424]. In particular they proved that given a purely unrectifiable compact set S ⊆ R2, one can construct a C-Lagrangian with a given superlinearity such that the universal singular set of L contains S. We show the natural generalization: That given an Fσ purely unrectifiable subset of the plane, one can construct a C-Lagrangian, of arbitrary superlinearity, with universal singular set covering this subset.

Original languageEnglish
Pages (from-to)179-197
Number of pages19
JournalZeitschrift fur Analysis und ihre Anwendung
Issue number2
Publication statusPublished - 8 Apr 2013


  • Partial regularity
  • Purely unrectifiable set
  • Universal singular set


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