2013/05/16 by Kamil Mróz, Kamil Mroz, Alexander Strohmaier · 1 citation
Mathematics · #Eigenfunction #Eigenvalues and eigenvectors #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Hyperbolic function #Hyperbolic manifold #Laplace operator #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Metric (unit) #Point (geometry) #Pure mathematics #Remainder #Riemannian manifold #Spectral Theory in Mathematical Physics #TRACE (psycholinguistics) #Term (time) #math.SP #msc:35P15 #msc:35P20
paper · pdf · doi:10.1112/jlms/jdu010
published in Journal of the London Mathematical Society 89(3), 917-940 (Wiley) · 23 pages, 2 figures
arxiv created 2013/05/16 · openalex publication_date 2014/05/31 · arxiv updated 2015/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We derive explicit bounds for the remainder term in the local Weyl law for locally hyperbolic manifolds; we also give estimates of the derivative of this remainder. We use these to obtain explicit bounds for the C l norms of the L 2 -normalized eigenfunctions in the case that the spectrum of the Laplacian is discrete, for example, for closed Riemannian manifolds. We also derive bounds for the local heat trace. Our estimates are purely local and therefore also hold for any manifold at points near which the metric is locally hyperbolic.