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:
“In the case of our main stock of well-worn predicates, I submit that the judgment of projectibility has derived from the habitual projection, rather than the habitual projection from the judgment of projectibility. The reason why only the right predicates happen so luckily to have become well entrenched is just that the well entrenched predicates have thereby become the right ones.”
—Nelson Goodman (b. 1906)
“Without metaphor the handling of general concepts such as culture and civilization becomes impossible, and that of disease and disorder is the obvious one for the case in point. Is not crisis itself a concept we owe to Hippocrates? In the social and cultural domain no metaphor is more apt than the pathological one.”
—Johan Huizinga (1872–1945)
“I believe in the equality of man; and I believe that religious duties consist in doing justice, loving mercy, and endeavoring to make our fellow-creatures happy.”
—Thomas Paine (1737–1809)