  The analysis of axisymmetric spacetimes, dynamical or stationary, is usually
made in the reduced space. We prove here a stability property of the quo- tient
space and use it together with minimal surface techniques to constraint the
shape of General Relativistic bodies in terms of their energy and rotation.
These constraints are different in nature to the mechanical limitations that a
particular material body can have and which can forbid, for instance, rotation
faster than a certain rate, (after which the body falls apart). The relations
we are describing instead are fundamental and hold for all bodies, albeit they
are useful only in General Relativistic regimes. For Neutron stars they are
close to be optimal, and, although precise models for these stars display
tighter con- straints, our results are significative in that they do not depend
on the equation of state.
