Uniqueness of starshaped compact hypersurfaces with prescribed \(m\)-th mean curvature in hyperbolic space (Q2382963)

By applying the geometric form of Alexsandrov's maximum principle the authors prove uniqueness of solutions to the prescribed \(m\)-th elementary symmetric curvature problem in hyperbolic \(n\)-space. More precisely: Under conditions (involving \(C^2\) estimates) where existence has been proven by \textit{Q. Jin} and \textit{Y. Li} [Discrete Contin. Dyn. Syst. 15, No. 2, 367--377 (2006; Zbl 1177.53058)] it is shown that uniqueness (up to a geometrically trivial transformation) holds.