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Title:
Extensions of Riemannian manifolds and Bartnik mass estimates
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Abstract:
Recently, C. Mantoulidis and R. Schoen constructed asymptotically flat extensions with controlled ADM mass of Bartnik data $\mathcal{B} = (\S \cong \mathbb{S}^2,g,H=0)$, where $g$ is a metric satisfying $\lambda_1(-\Delta_g + K(g)) > 0$ and $K(g)$ denotes the Gauss curvature of $g$. In particular, they used these extensions to show that the Bartnik mass of $\mathcal{B}$ equals the optimal value in the Riemannian Penrose inequality. In this talk, we will present some results involving Bartnik mass estimates that were inspired by their construction. This talk is based on joint works with C. Cederbaum, S. McCormick and P. Miao.
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