  We prove that the norm-square of a moment map associated to a linear action
of a compact group on an affine variety satisfies a certain gradient
inequality. This allows us to bound the gradient flow, even if we do not assume
that the moment map is proper. We describe how this inequality can be extended
to hyperkahler moment maps in some cases, and use Morse theory with the
norm-squares of hyperkahler moment maps to compute the Betti numbers and
cohomology rings of all toric hyperkahler orbifolds.
