Math @ Duke

Publications [#287085] of Hubert Bray
Papers Published
 Bray, H; Morgan, F, An isoperimetric comparison theorem for schwarzschild space and other manifolds,
Proceedings of the American Mathematical Society, vol. 130 no. 5
(January, 2002),
pp. 14671472 [pdf], [doi]
(last updated on 2021/05/12)
Abstract: We give a very general isoperimetric comparison theorem which, as an important special case, gives hypotheses under which the spherically symmetric (n  1)spheres of a spherically symmetric nmanifold are isoperimetric hypersurfaces, meaning that they minimize (n  1)dimensional area among hypersurfaces enclosing the same nvolume. This result greatly generalizes the result of Bray (Ph.D. thesis, 1997), which proved that the spherically symmetric 2spheres of 3dimensional Schwarzschild space (which is defined to be a totally geodesic, spacelike slice of the usual (3 + 1)dimensional Schwarzsehild metric) are isoperimetric. We also note that this Schwarzschild result has applications to the Penrose inequality in general relativity, as described by Bray.


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