2008/02/20 by Bruno Colbois, Colbois, Bruno, Daniel Maerten +1
Computer Science · Mathematics · #35P15 #51F99 #53C99 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.DG #msc:35P15 #msc:51F99 #msc:53C99
paper · pdf · doi:10.48550/arxiv.0802.2774
9 pages, submitted december 2007
arxiv created 2008/02/20 · openalex publication_date 2008/02/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a bounded domain (with smooth boundary) in a given complete (not compact a priori) Riemannian manifold with Ricci bounded below . For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general metric way, interesting for itself. As application, we get upper bounds for the Neumann spectrum which is clearly in agreement with the Weyl law and which is analogous to Buser's upper bounds of the spectrum of a closed Riemannian manifold with lower bound on the Ricci curvature.