  We study the Riemannian quantiative isoperimetric inequality. We show that
direct analogue of the Euclidean quantitative isoperimetric inequality is--in
general--false on a closed Riemannian manifold. In spite of this, we show that
the inequality is true generically. Moreover, we show that a modified (but
sharp) version of the quantitative isoperimetric inequality holds for a real
analytic metric, using the Lojasiewicz-Simon inequality. A main novelty of our
work is that in all our results we do not require any a priori knowledge on the
structure/shape of the minimizers.
