Stable Constant Mean Curvature Tori and the Isoperimetric Problem in Three Space Forms

Let ψ: M → N be an immersion of an orientable surface into a three dimensional oriented Riemannian manifold. Then ψ has constant mean curvature if and only if it is a critical point of the area functional for any compactly supported variation that preserves the volume enclosed by the surface. In this context we say that th