The problem of isometric embedding of a positively curved 2-sphere in the Euclidean 3-space was considered by Hermann Weyl in 1916 and it's known as the classical Weyl problem. In this talk we consider (spacelike) isometric embeddings of a metric on the sphere into de Sitter space, with a suitable curvature restriction. We show a bound for the mean curvature H of such spacelike hypersurfaces in terms of the scalar curvature, its Laplacian, the dimension and a scaling factor of the ambient space. The proof uses geometric identities, and the maximum principle for a prescribed symmetric-curvature equation.

This is joint work with Ben Lambert and Wilhelm Klingenberg.