On the sharp interface limit of a phase field model for near spherical two phase biomembranes

We consider sharp interface asymptotics for a phase field model motivated by lipid raft formation on near spherical biomembranes involving coupling between the local mean curvature and composition. A reduced diffuse energy depending only membrane composition is introduced $\\Gamma$-limit derived. It shown that Euler–Lagrange equations limiting functional coincide. Finally, we system of gradient flow with conserved Allen–Cahn dynamics model. Performing formal asymptotic analysis, obtain geodesic to fourth order PDE free boundary problem surface deformation.