A phase field model with a geodesic distance penalty between curves Gamma-converges to Plateau's problem for a single curve on a cylinder, and gives numerical approximations in wider cases.
A cahn--hilliard--willmore phase field model for non-oriented interfaces, 2024
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Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach
A phase field model with a geodesic distance penalty between curves Gamma-converges to Plateau's problem for a single curve on a cylinder, and gives numerical approximations in wider cases.