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arXiv · 1305.1839

On the local rigidity of Einstein manifolds with convex boundary

Michael T Anderson
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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.

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Michael T Anderson. 2013-05-08. On the local rigidity of Einstein manifolds with convex boundary. https://arxiv.org/abs/1305.1839

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