Case of Equality
Both the Bray and Huisken-Ilmanen proofs of the Riemannian Penrose inequality state that under the hypotheses, if
then the manifold in question is isometric to a slice of the Schwarzschild spacetime outside of the outermost minimal surface.
Read more about this topic: Riemannian Penrose Inequality
Famous quotes containing the words case of, case and/or equality:
“I am absurdly fearful about this voyage. Various little omens have combined to give me a dark feeling.... Perhaps we shall live to laugh at these. But in case of mishap I should perish with my husband and child, perhaps to be transferred to some happier state.”
—Margaret Fuller (1810–1850)
“Sculpture and painting are very justly called liberal arts; a lively and strong imagination, together with a just observation, being absolutely necessary to excel in either; which, in my opinion, is by no means the case of music, though called a liberal art, and now in Italy placed even above the other two—a proof of the decline of that country.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“It is clear that not in one thing alone, but in many ways equality and freedom of speech are a good thing.”
—Herodotus (c. 484–424 B.C.)