  We study the dynamics of orientational phase ordering in fluid membranes.
Through numerical simulation we find an unusually slow coarsening of
topological texture, which is limited by subdiffusive propagation of membrane
curvature. The growth of the orientational correlation length $\xi$ obeys a
power law $\xi \propto t^w$ with $w < 1/4$ in the late stage. We also discuss
defect profiles and correlation patterns in terms of long-range interaction
mediated by curvature elasticity.
