We consider the intersection of a convex surface Γ with a periodic perforation of R d , which looks like a sieve, given by T ε = ⋃ k ∈ Z d { ε k + a ε T } where T is a given compact set and a ε ≪ ε is the size of the perforation in the ε -cell ( 0 , ε ) d ⊂ R d . When ε tends to zero we establish uniform estimates for p-capacity, 1 < p < d , of the set Γ ∩ T ε . Additionally, we prove that the intersections Γ ∩ { ε k + a ε T } k are uniformly distributed over Γ and give estimates for the discrepancy of the distribution. As an application we show that the thin obstacle problem with the obstacle defined on the intersection of Γ and the perforations, in a given bounded domain, is homogenizable when p < 1 + d 4 . This result is new even for the classical Laplace operator.