Starshaped Compact Hypersurfaces in Warped Product Manifolds II: A Class of Hessian Type Equations

Abstract

In this note, we prove the existence of one particular class of starshaped compact hypersurfaces, by deriving global curvature estimates for such hypersurfaces; this generalizes a recent result on this problem from the Euclidean space to Riemannian warped products. Moreover, we show that interior second order a priori estimates for admissible solutions to the associated fully nonlinear elliptic partial differential equations can be readily established by similar arguments.