An isoperimetric comparison theorem for schwarzschild space and other manifolds

Conference Paper

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 n-manifold are isoperimetric hypersurfaces, meaning that they minimize (n - 1)-dimensional area among hypersurfaces enclosing the same n-volume. This result greatly generalizes the result of Bray (Ph.D. thesis, 1997), which proved that the spherically symmetric 2-spheres of 3-dimensional Schwarzschild space (which is defined to be a totally geodesic, space-like 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.

Full Text

Duke Authors

Cited Authors

  • Bray, H; Morgan, F

Published Date

  • 2002

Published In

  • Proceedings of the American Mathematical Society

Volume / Issue

  • 130 / 5

Start / End Page

  • 1467 - 1472

Digital Object Identifier (DOI)

  • 10.1090/S0002-9939-01-06186-X