Kristály, A. (2018) Journal de Mathématiques Pures et Appliquées [Matematică, Q1]

Publicat: 24 Noiembrie 2020

Kristály, A. (2018) Sharp uncertainty principles on Riemannian manifolds: the influence of curvature. Journal de Mathématiques Pures et Appliquées, 119, 326-346.

DOI: https://doi.org/10.1016/j.matpur.2017.09.002

✓ Publisher: Elsevier
✓ Web of Science Core Collection: Science Citation Index Expanded
✓ Categories: Mathematics, Applied; Mathematics
✓ Article Influence Score (AIS): 2.366 (2018) / Q1 in all categories

Abstract: We present a rigidity scenario for complete Riemannian manifolds supporting the Heisenberg-Pauli-Weyl uncertainty principle with the sharp constant in R-n (shortly, sharp HPW principle). Our results deeply depend on the curvature of the Riemannian manifold which can be roughly formulated as follows: (a) When (M, g) has non-positive sectional curvature, the sharp HPW principle holds on (M, g). However, positive extremals exist in the sharp HPW principle if and only if (M, g) is isometric to R-n , n = dim(M). (b) When (M, g) has non-negative Ricci curvature, the sharp HPW principle holds on (M, g) if and only if (M, g) is isometric to R-n. Since the sharp HPW principle and the Hardy-Poincare inequality are endpoints of the Caffarelli-Kohn-Nirenberg interpolation inequality, we establish further quantitative results for the latter inequalities in terms of the curvature on Cartan- Hadamard manifolds.

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