Starshaped Compact Hypersurfaces with Prescribed M-th Mean Curvature in Elliptic Space (Journal of Partial Differential Equations, 2002)
We consider the problem of finding a compact starshaped hypresurface in a space form for which the normalized m-th elementary symmetric function of principal curvatures is a prescribed function. In this paper the conditions for the existence of at least one solution to a nonlinear second order elliptic equation of that problem are established in case of a space form with positive sectional curvature.
Keywords: Nonlinear elliptic equations; Spaces of constant sectional curvature; Hypersurfaces with prescribed curvature functions