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 and/or equality:
“I often used to think myself in the case of the fox-hunter, who, when he had toiled and sweated all day in the chase as if some unheard-of blessing was to crown his success, finds at last all he has got by his labor is a stinking nauseous animal. But my condition was yet worse than his; for he leaves the loathsome wretch to be torn by his hounds, whilst I was obliged to fondle mine, and meanly pretend him to be the object of my love.”
—Sarah Fielding (1710–1768)
“When I speak of The Case for Equality I mean human equality; and that, of course, can only mean one thing: it means equality of income.”
—George Bernard Shaw (1856–1950)