# 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