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Title:
A connection between Bartnik mass and Wang-Yau quasi-local mass
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Abstract:
We discuss some recent observation that ties the Bartnik mass to the generalized Wang-Yau quasi-local energy with respect to static spaces. More precisely, given a family of closed $2$-surfaces $\{\Sigma_t\}$ evolving in a $3$-manifold of nonnegative scalar curvature, if the reference static space of the generalized Wang-Yau quasi-local energy is a minimal mass extension of $\Sigma_0$, we observe that the derivative of the quasi-local energy of $\Sigma_t$ at $\Sigma_0$ agrees with the derivative of the Bartnik mass of $\Sigma_t$ at $\Sigma_0$. We also discuss its implication to the rigidity case of a localized Penrose inequality. This talk is based on joint work with Siyuan Lu.
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