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arXiv · 2009.02959

Mass of asymptotically flat $3$-manifolds with boundary

Sven Hirsch·Pengzi Miao·Tin-Yau Tsang
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Abstract

We study the mass of asymptotically flat $3$-manifolds with boundary using the method of Bray-Kazaras-Khuri-Stern. More precisely, we derive a mass formula on the union of an asymptotically flat manifold and fill-ins of its boundary, and give new sufficient conditions guaranteeing the positivity of the mass. Motivation to such consideration comes from studying the quasi-local mass of the boundary surface. If the boundary isometrically embeds in the Euclidean space, we apply the formula to obtain convergence of the Brown-York mass along large surfaces tending to $\infty$ which include the scaling of any fixed coordinate-convex surface.

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Sven Hirsch, Pengzi Miao, Tin-Yau Tsang. 2021-06-23. Mass of asymptotically flat $3$-manifolds with boundary. https://arxiv.org/abs/2009.02959

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