Curvature Estimates for Stable Minimal Triple Junction Surfaces

Abstract

In the well known work of Schoen-Simon-Yau, they gave the $L^p$ curvature estimate for stable minimal hypersurfaces in ${\mathbb{R}}^n$. Based on this estimate, they showed the Generalized Bernstein Theorem holds for stable minimal hypersurfaces when dimension is small. In this talk, I will show that these results can be generalized to stable minimal triple junction surfaces in some sense. As a corollary, giving some suitable conditions, we can show that generalized Bernstein Theorem holds in the case of stable minimal triple junction surfaces.