An isoperimetric comparison theorem (Q1207420)

The author discusses the isoperimetric inequality for a complete, simply connected, 3-dimensional Riemannian manifold \(M\) with sectional curvature \(K_ M\leq k\leq 0\). If \(E\subset M\) is a compact domain with smooth boundary \(\partial E\) and \(B\) is the geodesic ball in the 3-dimensional model space of constant curvature \(k\) with the same volume as \(E\), then \(\text{area}(\partial E)\geq\text{area}(\partial B)\) and equality holds iff \(E\) is isometric \(B\).