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 , one can construct a -Lagrangian with a given superlinearity such that the universal singular set of contains . We show the natural generalization: That given an purely unrectifiable subset of the plane, one can construct a -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. 179–197DOI 10.4171/ZAA/1480