  Giant planets can clear deep gaps when embedded in 2D (razor-thin) viscous
circumstellar disks. We show by direct simulation that giant planets are just
as capable of carving out gaps in 3D. Surface density maps are similar between
2D and 3D, even in detail. In particular, the scaling $\Sigma_{\rm gap} \propto
q^{-2}$ of gap surface density with planet mass, derived from a global
"zero-dimensional" balance of Lindblad and viscous torques, applies equally
well to results obtained at higher dimensions. Our 3D simulations reveal
extensive, near-sonic, meridional flows both inside and outside the gaps; these
large-scale circulations might bear on disk compositional gradients, in dust or
other chemical species. At high planet mass, gap edges are mildly Rayleigh
unstable and intermittently shed streams of material into the gap - less so in
3D than in 2D.
