Hsu, Yi-Jung; Shiau, Sheng-Jong; Wang, Tai-Ho Graphs with prescribed mean curvature in the sphere. (English) Zbl 0984.35064 Bull. Inst. Math., Acad. Sin. 28, No. 4, 215-223 (2000). 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 \({\mathcal H}\). Reviewer: Messoud Efendiev (Berlin) Cited in 1 Document MSC: 35J60 Nonlinear elliptic equations 53B20 Local Riemannian geometry 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions Keywords:Riemannian manifold PDFBibTeX XMLCite \textit{Y.-J. Hsu} et al., Bull. Inst. Math., Acad. Sin. 28, No. 4, 215--223 (2000; Zbl 0984.35064)