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Riemannian Penrose Inequality

The Riemannian Penrose inequality is the time-symmetric mass-area inequality for an asymptotically flat Riemannian manifold of nonnegative scalar curvature. For a minimal outer-minimizing boundary of total area A, its normalization in dimension n>=3 is

m_(ADM)>=1/2(A/(omega_(n-1)))^((n-2)/(n-1)).

A Schwarzschild-Tangherlini spatial metric attaining equality is

g=(1+m/(2r^(n-2)))^(4/(n-2))delta

for r>=(m/2)^(1/(n-2)), where its boundary has area omega_(n-1)(2m)^((n-1)/(n-2)).

See also

ADM Mass, Inverse Mean Curvature Flow, Minimal Surface, Penrose Inequality, Scalar Curvature, Schwarzschild Metric

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References

Bray, H. L. and Lee, D. A. "On the Riemannian Penrose Inequality in Dimensions Less than Eight." Duke Math. J. 148, 81-106, 2009. https://doi.org/10.1215/00127094-2009-020.

Cite this as:

Weisstein, Eric W. "Riemannian Penrose Inequality." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RiemannianPenroseInequality.html

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