Curvature estimates for stable minimal surfaces with a common free boundary

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The minimal surfaces meeting in triples with equal angles along a common boundary naturally arise from soap films and other physical phenomena. They are also the natural extension of the usual minimal surfaces. In this paper, we consider the multiple junction surface and show the Bernstein’s Theorem still holds for the stable multiple junction surfaces in some special cases. The key part is to derive the \(L^p\) estimates of the curvature for multiple junction surfaces.