Uniqueness of entire graphs in Riemannian warped products

Authors

JUNHONG DONG
XIMIN LIU

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.

DOI

10.3906/mat-1510-2

Keywords

Warped product, monotonic function, complete spacelike hypersurface, $r$-th mean curvature

First Page

1246

Last Page

1257

Recommended Citation

DONG, JUNHONG and LIU, XIMIN (2016) "Uniqueness of entire graphs in Riemannian warped products," Turkish Journal of Mathematics: Vol. 40: No. 6, Article 7. https://doi.org/10.3906/mat-1510-2
Available at: https://journals.tubitak.gov.tr/math/vol40/iss6/7