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?
$\begingroup$
$\endgroup$
1
-
3$\begingroup$ Is the hypersphere a minimal surface? $\endgroup$– Fan ZhengNov 3, 2017 at 5:07
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
No: consider the catenoid in euclidean 3-space and intersect it with a plane which is perpendicular to the symmetry axis of the catenoid. The intersection is a circle, which is not s geodesic (minimal surface of dimension 1).
