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For an admissible class of smooth compact initial data sets with boundary, we prove a comparison theorem between the Wang/Liu-Yau quasi-local mass of the boundary and the Hawking mass of strictly minimizing hulls in the Jang graphs of the domain.
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2006
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2007
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2009
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A. Alaee, K. Khuri, and S.-T. Yau, Geometric Inequalities for quasi-local masses
2020
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Y. Shi, and L.-F. Tam, Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature
2002
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J. Corvino, A note on asymptotically flat metrics on ℝ 3 \mathbb{R}^{3} which are scalar-flat and admit minimal spheres
2005
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A. Alaee, A.Cabrera Pacheco, S. McCormick, Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space
2021
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