On the Gauss map of an area-minimizing hypersurface
Let S be an area-minimizing hypersurface of \({\mathbb{R}}^ N\). In the 1960's it was discovered that the dimensional restriction \(N<8\) guarantees to S several very strong properties which fail to hold as soon as \(N\geq 8\). The most important two of these properties are the interior regularity and the Bernstein property. In the present paper the author shows that the dimensional hypothesis \(N<8\) can be replaced by a different condition which involves the topology and the Gauss image of S and which guarantees both properties independent of dimension. In the case of minimal surfaces a similar condition on the Gauss map appeared in a conjecture of Nirenberg which was proved by R. Osserman.
scientific article; zbMATH DE number 3874158