  Gap formation by giant planets in self-gravitating disks may lead to a
gravitational edge instability (GEI). We demonstrate this GEI with global 3D
and 2D self-gravitating disk-planet simulations using the ZEUS, PLUTO and FARGO
hydrodynamic codes. High resolution 2D simulations show that an unstable outer
gap edge can lead to outwards orbital migration. Our results have important
implications for theories of giant planet formation in massive disks.
