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Journal of Convex Analysis 08 (2001), No. 1, 269--278
Copyright Heldermann Verlag 2001

Semiconvex Hulls of Quasiconformal Sets

Baisheng Yan
Dept. of Mathematics, Michigan State University, East Lansing, MI 48824, U.S.A.

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 Rn", 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.

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