Prescribed Weingarten curvature equations in warped product manifolds
Differential Geometry
2021-11-30 v2
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 -th Weingarten curvature satisfies some constraint) in a given warped product manifold of special type can be assured.
Keywords
Cite
@article{arxiv.2111.01636,
title = {Prescribed Weingarten curvature equations in warped product manifolds},
author = {Ya Gao and Chenyang Liu and Jing Mao},
journal= {arXiv preprint arXiv:2111.01636},
year = {2021}
}
Comments
19 pages. Two minor typos in Introduction (of v1) have been corrected, and the latest status of reference [2] has been updated. Comments are welcome