  We consider finite deformations of the p+2-dimensional Schwarzschild geometry
which obey the vacuum Einstein equation, preserve the mean curvature and
induced conformal metric on a sphere a distance $\lambda$ from the horizon and
are regular on the future horizon. We show perturbatively that in the limit
$\lambda$ approaches 0 the deformations are given by solutions of the nonlinear
incompressible Navier-Stokes equation on the p-sphere. This relation provides a
link between global existence for p-dimensional incompressible Navier-Stokes
fluids and a novel form of cosmic censorship in p+2-dimensional general
relativity.
