Spectral cluster bounds for orthonormal functions on manifolds with nonsmooth metrics

2025/05/09 by Jean‐Claude Cuenin, Cuenin, Jean-Claude, Ngoc Nhi Nguyen +3
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2505.05904

openalex publication_date 2025/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish L^q spectral cluster bounds for families of orthonormal functions associated to the Laplace-Beltrami operator on a compact Riemannian manifold. The metric is only assumed to be of class C^s, where 0≤ s≤ 2.

Citations

• Orthonormal Strichartz estimate for dispersive equations with potentials
• Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates
• The orthonormal Strichartz inequality on torus
• On the Strichartz estimates for orthonormal systems of initial data with regularity
• Spectral cluster bounds for orthonormal systems and oscillatory integral\n operators in Schatten spaces
• Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates
• Sharp L^p bounds on spectral clusters for Lipschitz metrics
• Strichartz estimates for the kinetic transport equation
• Dispersive estimates for principally normal pseudodifferential operators

Related

• Spectral cluster bounds for orthonormal systems and oscillatory integral\n operators in Schatten spaces
• Sharp Spectral-Cluster Restriction Bounds for Orthonormal Systems
• Improved Spectral Cluster Bounds for Orthonormal Systems
• Neumann spectral cluster estimates outside convex obstacles
• Sharp L^p bounds on spectral clusters for Lipschitz metrics