Uncertainty Principle and its rigidity on complete gradient shrinking Ricci solitons

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 addtion, we partially give analogous rigidity results of the Caffarelli-Kohn-Nirenberg inequalities on shrinking Ricci solitons.

References in corpus (1)

• A lower bound for the scalar curvature of noncompact nonflat Ricci shrinkers