Riemannian Penrose Inequality - Case of Equality

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:

    It was a maxim with Mr. Brass that the habit of paying compliments kept a man’s tongue oiled without any expense; and that, as that useful member ought never to grow rusty or creak in turning on its hinges in the case of a practitioner of the law, in whom it should be always glib and easy, he lost few opportunities of improving himself by the utterance of handsome speeches and eulogistic expressions
    Charles Dickens (1812–1870)

    Instructing in cures, therapists always recommend that “each case be individualized.” If this advice is followed, one becomes persuaded that those means recommended in textbooks as the best, means perfectly appropriate for the template case, turn out to be completely unsuitable in individual cases.
    Anton Pavlovich Chekhov (1860–1904)

    You can’t protect women without handicapping them in competition with men. If you demand equality you must accept equality. Women can’t have it both ways.
    —Mary Bell-Richards. “Protective Legislation in England,” Equal Rights (October 3, 1925)