Uncertainty principle and its rigidity on complete gradient shrinking Ricci solitons

Mai, Weixiong; Ou, Jianyu

doi:10.1090/proc/15210

Uncertainty principle and its rigidity on complete gradient shrinking Ricci solitons
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by Weixiong Mai and Jianyu Ou

Proc. Amer. Math. Soc. 149 (2021), 285-299

DOI: https://doi.org/10.1090/proc/15210

Published electronically: October 20, 2020

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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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