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Uncertainty principle and its rigidity on complete gradient shrinking Ricci solitons


Authors: Weixiong Mai and Jianyu Ou
Journal: Proc. Amer. Math. Soc. 149 (2021), 285-299
MSC (2010): Primary 26D10, 53C21, 53C24
DOI: https://doi.org/10.1090/proc/15210
Published electronically: October 20, 2020
MathSciNet review: 4172605
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Abstract: We prove rigidity theorems for shrinking gradient Ricci solitons supporting the Heisenberg-Pauli-Weyl uncertainty principle with the sharp constant in $\mathbb {R}^n$. In addition, we partially give analogous rigidity results of the Caffarelli-Kohn-Nirenberg inequalities on shrinking Ricci solitons.


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Additional Information

Weixiong Mai
Affiliation: School of Mathematics (Zhuhai), Sun Yat-Sen University (Zhuhai), Zhuhai, People’s Republic of China
MR Author ID: 1079061
Email: maiwx3@mail.sysu.edu.cn

Jianyu Ou
Affiliation: Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, People’s Republic of China
Email: oujianyu@fudan.edu.cn

Received by editor(s): December 28, 2019
Received by editor(s) in revised form: May 26, 2020
Published electronically: October 20, 2020
Additional Notes: The first author was partially supported by National Natural Science Foundation of China No. 11901594, and the Fundamental Research Fund for the Central Universities (20lgpy150).
The second author was partially supported by China’s post-doctoral fund special support No. KLH1411067, and China’s post-doctoral fund support No. KLH1414010.
The second author is the corresponding author.
Communicated by: Guofang Wei
Article copyright: © Copyright 2020 American Mathematical Society