Sup-norm Estimates for $overline{partial}$ in $mathbb{C}^3$

We develop a method for proving sup-norm and Holder estimates for $overline{partial}$ on wide class of finite type pseudoconvex domains in $mathbb{C}^n$. A fundamental obstruction to proving sup-norm estimates is the possibility of singular complex curves with exceptionally high order of contact with the boundary. Our method handles this problem, and in $mathbb{C}^3$, we prove sup-norm and Holder estimates for all bounded, pseudoconvex domains with real-analytic boundary.