Below are two alternative ways to express the problem:
Let the (n − 1) sphere be embedded as a minimal hypersurface in 
(1). Is it necessarily an equator?
By the Almgren–Calabi theorem, it's true when n = 3 (or n = 2 for the 1st formulation).
Wu-Yi Hsiang proved it for n ∈ {4, 5, 6, 7, 8, 10, 12, 14} (or n ∈ {3, 4, 5, 6, 7, 9, 11, 13}, respectively)
In 1987, Per Tomter proved it for all even n (or all odd n, respectively).
Thus, it only remains unknown for all odd n ≥ 9 (or all even n ≥ 8, respectively)
Is it true that an embedded, minimal hypersphere inside the Euclidean 
-sphere is
necessarily an equator?
Geometrically, the problem is analogous to the following problem:
Is the local topology at an isolated singular point of a minimal hypersurface necessarily different from that of a disc?
For example, the affirmative answer for spherical Bernstein problem when n = 3 is equivalent to the fact that the local topology at an isolated singular point of any minimal hypersurface in an arbitrary Riemannian 4-manifold must be different from that of a disc.
