The weyl problem in warped product spaces

Chunhe Li School of Mathematical Sciences, University of Electronic Science and Technology of China Zhizhang Wang School of Mathematical Sciences, Fudan Univeristy

Analysis of PDEs Differential Geometry mathscidoc:2103.03006

Journal of Differential Geometry, 114, (2), 243-304, 2020.2
In this paper, we discuss the Weyl problem in warped product spaces. We apply the method of continuity and prove the openness of the Weyl problem. A counterexample is constructed to show that the isometric embedding of the sphere with canonical metric is not unique up to an isometry if the ambient warped product space is not a space form. Then, we study the rigidity of the standard sphere if we fi x its geometric center in the ambient space. Finally, we discuss a Shi-Tam type of inequality for the Schwarzschild manifold as an application of our findings.
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@inproceedings{chunhe2020the,
  title={THE WEYL PROBLEM IN WARPED PRODUCT SPACES},
  author={Chunhe Li, and Zhizhang Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210328122214932125770},
  booktitle={Journal of Differential Geometry},
  volume={114},
  number={2},
  pages={243-304},
  year={2020},
}
Chunhe Li, and Zhizhang Wang. THE WEYL PROBLEM IN WARPED PRODUCT SPACES. 2020. Vol. 114. In Journal of Differential Geometry. pp.243-304. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210328122214932125770.
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