  Let (M, g) be a compact Einstein manifold with non-empty boundary. We prove
that Killing fields at the boundary extend to Killing fields of any (M, g)
provided the boundary is weakly convex and a simple condition on the
fundamental group holds. This gives a new proof of the classical infinitesimal
rigidity of convex surfaces in Euclidean space and generalizes the result to
Einstein metrics of any dimension.
