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We consider the intersection of a convex surface $\Ga$ with a periodicperforation of $\R^d$, which looks like a sieve, given by $T_\e = \bigcup_{k\in\Z^d}\{\e k+a_\e T\}$ where $T$ is a given compact set and $a_\e\ll \e$ is thesize of the perforation in the $\e$-cell $(0, \e)^d\subset \R^d$. When $\e$tends to zero we establish uniform estimates for $p$-capacity $1<p<d$ anddiscrepancy of distributions of intersection $\Ga\cap T_\e$. As an applicationone gets that the thin obstacle problem with the obstacle defined on theintersection of $\Ga$ and perforations, in given bounded domain, ishomogenizable when $p<1+\frac d4$. This result is new even for the classicalLaplace operator.

Estimates for capacity and discrepancy of convex surfaces in sieve-like domains with an application to homogenization