Suppose we have a compact Riemannian manifold $(M,g)$, and a Morse function $f : M \rightarrow \mathbb{R}$. Suppose we consider the gradient flow generated by this function, i.e. $$\dot{x_t} = - \nabla f(x_t).$$

By Morse theory, this flow will converge to a critical point of $f$, and only local minima of $f$ will have basins of attraction with positive volume. How does one go about estimating the actual volume of these basins in terms of $f$ or its derivatives?