Uniqueness of entire graphs in Riemannian warped products

Authors : Junhong Dong, Ximin Liu

Pages : 1246-1257

View : 10 | Download : 8

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :In this paper, by applying the generalized Omori-Yau maximum principle for complete spacelike hypersurfaces in warped product spaces, we obtain the sign relationship between the derivative of warping function and support function. Afterwards, by using this result and imposing suitable restrictions on the higher order mean curvatures, we establish uniqueness results for the entire graph in a Riemannian warped product space, which has a strictly monotone warping function. Furthermore, applications to such a space are given.
Keywords : Warped product, monotonic function, complete spacelike hypersurface, $r$-th mean curvature