An isoperimetric comparison theorem for Schwarzschild space and other manifolds (Q2781307)

It is known that the use of polar coordinates gives a Riemannian metric a warped product form whereby the radial coordinate \(r\) defines a one-dimensional factor. The present paper compares the areas of sphere-like slices \(r=\text{const.}\) in such warped product manifolds and derives some new isoperimetric comparison theorem which applies to various situations: surfaces of revolution, cones, spacelike foliations of a spacetime, geodesic spheres in a spherically symmetric manifold.