English

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 kk-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