Title: Toroidal trapped surfaces and isoperimetric inequalities,
Abstract: We analytically construct an infinite number of trapped toroids in
spherically symmetric Cauchy hypersurfaces of the Einstein equations. We focus
on initial data which represent "constant density stars" momentarily at rest.
There exists an infinite number of constant mean curvature tori, but we also
deal with more general configurations. The marginally trapped toroids have been
found analytically and numerically; they are unstable. The topologically
toroidal trapped surfaces appear in a finite region surrounded by the
Schwarzschild horizon.