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:
“Religion is love; in no case is it logic.”
—Beatrice Potter Webb (1858–1943)
“When a bachelor of philosophy from the Antilles refuses to apply for certification as a teacher on the grounds of his color I say that philosophy has never saved anyone. When someone else strives and strains to prove to me that black men are as intelligent as white men I say that intelligence has never saved anyone: and that is true, for, if philosophy and intelligence are invoked to proclaim the equality of men, they have also been employed to justify the extermination of men.”
—Frantz Fanon (1925–1961)