Prescribed Weingarten curvature equations in warped product manifolds

Abstract

In this paper, under suitable settings, we can obtain the existence of solutions to a class of prescribed Weingarten curvature equations in warped product manifolds of special type by the standard degree theory based on the a priori estimates for the solutions. This is to say that the existence of closed hypersurface (which is graphic with respect to the base manifold and whose $k$-th Weingarten curvature satisfies some constraint) in a given warped product manifold of special type can be assured.

arXiv comment19 pages. Two minor typos in Introduction (of v1) have been corrected, and the latest status of reference [2] has been updated. Comments are welcome

References in corpus (2)

• Eigenvalue inequalities for the p-Laplacian on a Riemannian manifold and estimates for the heat kernel
• A class of curvature type equations