Abstract

We obtain the isoperimetric profile for the standard initial slices in the Reissner–Nordstrom and Schwarzschild anti-de Sitter spacetimes, following recent work of Bray and Morgan on isoperimetric comparison. We then discuss these results in the context of Bray’s isoperimetric approach to the Penrose inequality.

Keywords

differential geometry, isoperimetric problem, general relativity

Mathematical Subject Classification

Primary: 53C21, 83C99

Milestones

Received: 3 January 2006
Revised: 2 March 2007
Accepted: 7 March 2007

Authors