February 2020 The Weyl problem in warped product spaces
Chunhe Li, Zhizhang Wang
Author Affiliations +
J. Differential Geom. 114(2): 243-304 (February 2020). DOI: 10.4310/jdg/1580526016

Abstract

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 fixed 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.

Funding Statement

The first author’s research was supported partially by NSFC Grant No. 11871160.
The second author’s research was supported by NSFC Grant No. 11301087.

Citation

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Chunhe Li. Zhizhang Wang. "The Weyl problem in warped product spaces." J. Differential Geom. 114 (2) 243 - 304, February 2020. https://doi.org/10.4310/jdg/1580526016

Information

Received: 12 April 2016; Published: February 2020
First available in Project Euclid: 1 February 2020

zbMATH: 07163292
MathSciNet: MR4058963
Digital Object Identifier: 10.4310/jdg/1580526016

Rights: Copyright © 2020 Lehigh University

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Vol.114 • No. 2 • February 2020
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