A combined flow of maps and domain metrics is constructed to converge to half-harmonic boundary maps whose harmonic extensions are free boundary branched minimal immersions.
Wright,Uniqueness of Weak Solutions of the Plateau Flow, Calculus of Variations and Partial Differential Equations63(2024), article 152
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Flowing to free boundary minimal surfaces
A combined flow of maps and domain metrics is constructed to converge to half-harmonic boundary maps whose harmonic extensions are free boundary branched minimal immersions.