  Reaction-diffusion models with nonlocal constraints naturally arise as
limiting cases of coupled bulk-surface models of intracellular signalling. In
this paper, a minimal, mass-conserving model of cell-polarization on a curved
membrane is analyzed in the limit of slow surface diffusion. Using the tools of
formal asymptotics and calculus of variations, we study the characteristic
wave-pinning behavior of this system on three dynamical timescales. On the
short timescale, generation of an interface separating high- and
low-concentration domains is established under suitable conditions.
Intermediate timescale dynamics is shown to lead to a uniform growth or
shrinking of these domains to sizes which are fixed by global parameters.
Finally, the long time dynamics reduces to area-preserving geodesic curvature
flow that may lead to multi-interface steady state solutions. These results
provide a foundation for studying cell polarization and related phenomena in
biologically relevant geometries.
