  We propose a new Riemannian gradient descent method for computing spherical
area-preserving mappings of topological spheres using a Riemannian
retraction-based framework with theoretically guaranteed convergence. The
objective function is based on the stretch energy functional, and the
minimization is constrained on a power manifold of unit spheres embedded in
3-dimensional Euclidean space. Numerical experiments on several mesh models
demonstrate the accuracy and stability of the proposed framework. Comparisons
with two existing state-of-the-art methods for computing area-preserving
mappings demonstrate that our algorithm is both competitive and more efficient.
Finally, we present a concrete application to the problem of landmark-aligned
surface registration of two brain models.
