Closed Weingarten hypersurfaces in warped product manifolds J. BarbosaFrancisco de AndradeJorge de Lira 53C4235J60prescribed curvaturenonlinear elliptic PDEdegree theory Given a compact Riemannian manifold $M$, we consider a warped product $\bar{M} = I \times_{h}M$ where $I$ is an open interval in $\mathbb{R}$. We suppose that the mean curvature of the fibers does not change sign. Given a positive differentiable function $\psi$ in $\bar{M}$, we find a closed hypersurface $\Sigma$ which is solution of an equation of the form $F(B) = \psi$, where $B$ is the second fundamental form of $\Sigma$ and $F$ is a function satisfying certain structural properties. As examples, we may exhibit examples of hypersurfaces with prescribed higher order mean curvature. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3631 10.1512/iumj.2009.58.3631 en Indiana Univ. Math. J. 58 (2009) 1691 - 1718 state-of-the-art mathematics http://iumj.org/access/