On the local rigidity of Einstein manifolds with convex boundary

Abstract

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.

withdrawn for reconstruction; error in "stability argument" on p.13

References in corpus (3)

• Unique continuation results for Ricci curvature and applications
• On the Bartnik extension problem for the static vacuum Einstein equations
• Infinitesimal rigidity of convex surfaces through the second derivative of the Hilbert-Einstein functional I: Polyhedral case