J. Aust. Math. Soc.  80 (2006), 375-382
The double cover relative to a convex domain and the relative isoperimetric inequality

 Jaigyoung Choe   Department of Mathematics  Seoul National University  Seoul 151-742  Korea   choe@math.snu.ac.kr

Abstract
We prove that a domain in the exterior of a convex domain in a four-dimensional simply connected Riemannian manifold of nonpositive sectional curvature satisfies the relative isoperimetric inequality . Equality holds if and only if is an Euclidean half ball and is a hemisphere.