JournalszaaVol. 32, No. 2pp. 179–197

Universal Singular Sets and Unrectifiability

  • Richard Gratwick

    St. John's College, Oxford, UK
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The geometry of universal singular sets has recently been studied by M.Cs\"ornyei et al.[Arch.~Ration.~Mech.~Anal. 190 (2008)(3), 371–424]. In particular they proved that given a purely unrectifiable compact set SR2S \subseteq \mathbb{R}^2, one can construct a CC^{\infty}-Lagrangian with a given superlinearity such that the universal singular set of LL contains SS. We show the natural generalization: That given an FσF_{\sigma} purely unrectifiable subset of the plane, one can construct a CC^{\infty}-Lagrangian, of arbitrary superlinearity, with universal singular set covering this subset.

Cite this article

Richard Gratwick, Universal Singular Sets and Unrectifiability. Z. Anal. Anwend. 32 (2013), no. 2, pp. 179–197

DOI 10.4171/ZAA/1480