  We study local structure of the moduli space of compact Einstein metrics with
respect to the boundary conformal metric and mean curvature. In dimension
three, we confirm M. Anderson's conjecture in a strong sense, showing that the
map from Einstein metrics to such boundary data is generically a local
diffeomorphism. In dimensions greater than three, we obtain similar results for
Ricci flat metrics and negative Einstein metrics under new non-degenerate
boundary conditions.
