Integral of scalar curvature on manifolds with a pole
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- by Guoyi Xu;
- Proc. Amer. Math. Soc. 152 (2024), 4865-4872
- DOI: https://doi.org/10.1090/proc/16584
- Published electronically: September 20, 2024
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Abstract:
On any complete three dimensional Riemannian manifold with a pole and non-negative Ricci curvature, we show that the asymptotic scaling invariant integral of scalar curvature is equal to a term determined by the asymptotic volume ratio of this Riemannian manifold.References
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Bibliographic Information
- Guoyi Xu
- Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
- ORCID: 0000-0002-2603-5119
- Email: guoyixu@tsinghua.edu.cn
- Received by editor(s): May 15, 2023
- Received by editor(s) in revised form: June 11, 2023
- Published electronically: September 20, 2024
- Additional Notes: The author was partially supported by Beijing Natural Science Foundation Z190003, NSFC 11771230 and NSFC 12141103
- Communicated by: Jiaping Wang
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 4865-4872
- MSC (2020): Primary 53C20, 53C21
- DOI: https://doi.org/10.1090/proc/16584
- MathSciNet review: 4802637