On a Penrose-like inequality in dimensions less than eight

@article{McCormick2017OnAP,
  title={On a Penrose-like inequality in dimensions less than eight},
  author={S. McCormick and P. Miao},
  journal={arXiv: Differential Geometry},
  year={2017}
}
  • S. McCormick, P. Miao
  • Published 2017
  • Mathematics, Physics
  • arXiv: Differential Geometry
  • On an asymptotically flat manifold $M^n$ with nonnegative scalar curvature, with outer minimizing boundary $\Sigma$, we prove a Penrose-like inequality in dimensions $ n < 8$, under suitable assumptions on the mean curvature and the scalar curvature of $ \Sigma$. 
    15 Citations
    On a minkowski-like inequality for asymptotically flat static manifolds
    • 8
    • PDF
    On the rigidity of Riemannian–Penrose inequality for asymptotically flat 3-manifolds with corners
    • 8
    • Highly Influenced
    • PDF
    Rigidity of Riemannian Penrose inequality with corners and its implications
    Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature
    • 14
    • PDF
    Gluing Bartnik extensions, continuity of the Bartnik mass, and the equivalence of definitions
    • 4
    • PDF
    On the Fill-in of Nonnegative Scalar Curvature Metrics
    • 7
    • PDF
    Quasi-local Penrose inequalities with electric charge

    References

    SHOWING 1-10 OF 16 REFERENCES
    On the Riemannian Penrose inequality in dimensions less than 8
    • 93
    • Highly Influential
    • PDF
    Positive Mass Theorem on Manifolds admitting Corners along a Hypersurface
    • 136
    • PDF
    The inverse mean curvature flow and the Riemannian Penrose Inequality
    • 617
    • Highly Influential
    • PDF
    The mass of an asymptotically flat manifold
    • 612
    • PDF
    On compact $3$-manifolds with nonnegative scalar curvature with a CMC boundary component
    • 9
    • PDF
    On a Localized Riemannian Penrose Inequality
    • 22
    • PDF
    PROOF OF THE RIEMANNIAN PENROSE INEQUALITY USING THE POSITIVE MASS THEOREM
    • 343
    • Highly Influential
    • PDF
    Positive Mass Theorem and the Boundary Behaviors of Compact Manifolds with Nonnegative Scalar Curvature
    • 205
    • PDF
    On the proof of the positive mass conjecture in general relativity
    • 971
    • PDF