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- W2029634547 abstract "We study rigidity of minimal two-spheres $Sigma$ that locally maximize the Hawking mass on a Riemannian three-manifold with a positive lower bound on its scalar curvature. After assuming strict stability of $Sigma$, we prove that a neighborhood of it in $M$ is isometric to one of the deSitter-Schwarzschild metrics on $(- epsilon,epsilon)times Sigma$. We also show that if $Sigma$ is a critical point for the Hawking mass on the deSitter-Schwarzschild manifold $mathbb{R}timesSph^2$ and can be written as a graph over a slice $Sigma_r={r}timesmathbb{S}^2$, then $Sigma$ itself must be a slice, and moreover that slices are indeed local maxima amongst competitors that are graphs with small $C^2$-norm." @default.
- W2029634547 created "2016-06-24" @default.
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- W2029634547 date "2012-06-24" @default.
- W2029634547 modified "2023-09-27" @default.
- W2029634547 title "Hawking mass and local rigidity of minimal two-spheres in three-manifolds" @default.
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