Conditions for equality of hulls in the calculus of variations

We simplify and sharpen several results by K. Zhang concerning properties of quasiconvex hulls of sets and quasiconvex envelopes of their distance functions. The approach emphasizes the underlying geometry and in particular we show that Kpc = Kc implies Krc = Kc if and only if min(m, n) ≦ 2 thus answering a question raised in [Z2].