Semiconvex Hulls of Quasiconformal Sets

We make some remarks concerning the p-semiconvex hulls of the quasiconformal sets, using a recent significant observation of T. Iwaniec ["Nonlinear Cauchy-Riemann operators in R ⁿ ", Trans. Am. Math. Soc. 354 (2002) 1961–1995] on the important relation between the regularity of quasiregular mappings in the theory of geometric functions and the notion of Morrey's quasiconvexity in the calculus of variations. We also point out several partial results on a conjecture in that paper