Sharp uncertainty principles on Riemannian manifolds: the influence of curvature

DOI10.1016/j.matpur.2017.09.002zbMath1405.53056arXiv1311.6418OpenAlexW2963320407WikidataQ115343526 ScholiaQ115343526MaRDI QIDQ1791743

Alexandru Kristály

Publication date: 11 October 2018

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.6418

zbMATH Keywords

Riemannian manifoldcurvaturesharp constantHeisenberg-Pauli-Weyl uncertainty principle

Mathematics Subject Classification ID

Applications of global differential geometry to the sciences (53C80) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (21)

Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs ⋮ Sharp Hardy inequalities via Riemannian submanifolds ⋮ Sharp second order uncertainty principles ⋮ Improved Poincaré-Hardy inequalities on certain subspaces of the Sobolev space ⋮ Some rigidity results for Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds ⋮ Sharp Morrey–Sobolev inequalities and eigenvalue problems on Riemannian–Finsler manifolds with nonnegative Ricci curvature ⋮ On some strong Poincaré inequalities on Riemannian models and their improvements ⋮ An uncertainty principle on the Lorentz spaces ⋮ Improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principle ⋮ Sharp uncertainty principles on general Finsler manifolds ⋮ Interpolation between Brezis-Vázquez and Poincaré inequalities on nonnegatively curved spaces: sharpness and rigidities ⋮ An optimal improvement for the Hardy inequality on the hyperbolic space and related manifolds ⋮ Uncertainty principle and its rigidity on complete gradient shrinking Ricci solitons ⋮ Poincaré and Hardy Inequalities on Homogeneous Trees ⋮ General weighted Hardy-type inequalities related to Greiner operators ⋮ New sharp Hardy and Rellich type inequalities on Cartan–Hadamard manifolds and their improvements ⋮ \(L^p\)-uncertainty principle via fractional Schrödinger equation ⋮ Elliptic differential inclusions on non-compact Riemannian manifolds ⋮ Sharp Caffarelli–Kohn–Nirenberg inequalities on Riemannian manifolds: the influence of curvature ⋮ An extension problem and Hardy's inequality for the fractional Laplace-Beltrami operator on Riemannian symmetric spaces of noncompact type ⋮ Geometric Hardy inequalities via integration on flows

Cites Work

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• Caffarelli-Kohn-Nirenberg inequality on metric measure spaces with applications
• Sharp Poincaré-Hardy and Poincaré-Rellich inequalities on the hyperbolic space
• Bessel pairs and optimal Hardy and Hardy-Rellich inequalities
• Hardy inequalities on Riemannian manifolds and applications
• Comparison theorems in Finsler geometry and their applications
• Uncertainty principles on compact Riemannian manifolds
• Weighted Sobolev inequalities and Ricci flat manifolds
• Meilleures constantes dans le théorème d'inclusion de Sobolev et un théorème de Fredholm non linéaire pour la transformation conforme de la courbure scalaire
• Generalized uncertainty principles on spaces of homogeneous type
• The uncertainty principle: A mathematical survey
• Volume comparison and its applications in Riemann-Finsler geometry
• Hardy inequalities on non-compact Riemannian manifolds
• On the structure of spaces with Ricci curvature bounded below. I
• Caffarelli--Kohn--Nirenberg inequalities with remainder terms.
• Optimizing improved Hardy inequalities
• Improved \(L^p\)-Poincaré inequalities on the hyperbolic space
• Heisenberg-Pauli-Weyl uncertainty inequalities and polynomial volume growth
• The Caffarelli-Kohn-Nirenberg inequalities on complete manifolds
• An improved Hardy-Sobolev inequality and its application
• Hardy-Poincaré, Rellich and uncertainty principle inequalities on Riemannian manifolds
• A Universal Volume Comparison Theorem for Finsler Manifolds and Related Results
• The uncertainty principle
• On the best possible remaining term in the Hardy inequality
• Hardy's uncertainty principle on hyperbolic spaces
• Weighted Poincaré inequality and rigidity of complete manifolds
• Weak uncertainty principle for fractals, graphs and metric measure spaces
• Improved Hardy and Rellich inequalities on Riemannian manifolds
• A unified approach to improved $L^p$ Hardy inequalities with best constants
• $L^p$ versions of Hardy’s uncertainty principle on hyperbolic spaces
• Complete manifolds with non-negative Ricci curvature and the Caffarelli–Kohn–Nirenberg inequalities
• HARDY INEQUALITIES ON RIEMANNIAN MANIFOLDS WITH NEGATIVE CURVATURE

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