Starshaped compact hypersurfaces with prescribed M-th mean curvature in elliptic space

摘要

We consider the problem of finding a compact starshaped hypersurface in a space form for which the normalized m-th elementary symmetric function of prin- cipal 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.