Graphs with prescribed mean curvature in the sphere (Q2716801)

This paper is devoted to the following problem: is there an embedding \(Y\) from an \(n\)-dimensional Riemannian manifold \(M\) into an \((n+1)\)-dimensional Riemannian manifold \(N\) whose mean curvature is prescribed by function \({\mathcal H}\)? The authors show that for a given function \({\mathcal H}\) on the unit sphere \(S^{n+1}\), there is a unique group over the \(n\)-dimensional unit sphere whose mean curvature coincides with \({\mathcal H}\).