2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168305We consider a system of three surfaces, graphs over a bounded domain in ${\mathbb R}^2$, intersecting along a time-dependent curve and moving by mean curvature while preserving the pairwise angles at the curve of intersection (equal to $2π/3$.) For the corresponding two-dimensional parabolic free boundary problem we prove short-time existence of classical solutions (in parabolic Hölder spaces), for sufficiently regular initial data satisfying a compatibility condition.31 pages, submittedAnalysis of PDEsDifferential Geometrytext