We approach the problem of unfolding the surface of the cerebral cortex by modeling the problem as a front propagation governed by a Partial Different- ial Equation (PDE) which is solved using level set techniques. As a first step in this direction, we present multi-scale representations of closed surfaces that preserve their total area or enclosed volume. This is the three-dimensional extension of previous work on curves [21]. The resulting evolution equations allow the smoothing of closed surfaces without shrinkage. Additionally, correspondences between points in the surface at different scales are maintained by tracking the points of an initial mesh by means of an Ordinary Differential Equation (ODE). This technique allows to give tangential velocities to those points, therefore permitting them to move under general (tangential plus normal) velocity fields. We present the level set implementation of the normalized three-dimensional mean curvature flows and provide experimental results by unfolding surfaces segmented from MRI images of the human brain.