The spherical Bernstein's problem is a possible generalization of the original Bernstein's problem in the field of global differential geometry, first proposed by Shiing-Shen Chern in 1969, and then later in 1970, during his plenary address at the International Congress of Mathematicians in Nice.
Additionally, the spherical Bernstein's problem, while itself a generalization of the original Bernstein's problem, can, too, be generalized further by replacing the ambient space
Below are two alternative ways to express the problem: Let the (n − 1) sphere be embedded as a minimal hypersurface in
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
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.