J. Aust. Math. Soc.
80 (2006), 375382

The double cover relative to a convex domain and the relative isoperimetric inequality

Jaigyoung Choe
Department of Mathematics
Seoul National University
Seoul 151742
Korea
choe@math.snu.ac.kr



Abstract

We prove that a domain
in the exterior of a convex domain
in a fourdimensional 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.

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