# Is the intersection of two minimal surfaces minimal?

Consider two $n$-dimensional minimal surfaces without boundary. Suppose they are embedded in some $\mathbb{R}^m$ in such a way that they intersect transversally. Is their intersection a minimal surface? For example, when two hyperspheres overlap, their intersection is another, lower dimensional hypersphere, which is minimal (notice I am only counting the intersection of the surfaces of the spheres, not the interiors). Is this true in general?

• Is the hypersphere a minimal surface? – Fan Zheng Nov 3 '17 at 5:07