Convergence to the Product of the Standard Spheres and Eigenvalues of the Laplacian

2020/07/31 by Masayuki Aino, RIKEN, Japan
Mathematics · #Analytic and geometric function theory #Convergence (economics) #Curvature #Eigenvalues and eigenvectors #Geometric Analysis and Curvature Flows #Geometry #Hausdorff space #Laplace operator #Mathematical analysis #Mathematics #Physics #Point processes and geometric inequalities #Product (mathematics) #Pure mathematics #Quantum mechanics #Ricci curvature #SPHERES #math.DG #math.MG #msc:53C20 #msc:58J50

paper · pdf · doi:10.3842/sigma.2021.017

published as SIGMA 17 (2021), 017, 29 pages

arxiv created 2021/02/24 · openalex publication_date 2021/02/24 · arxiv updated 2021/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show a Gromov-Hausdorff approximation to the product of the standard spheres for Riemannian manifolds with positive Ricci curvature under some pinching condition on the eigenvalues of the Laplacian acting on functions and forms.

Citations

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• Metric measure spaces with Riemannian Ricci curvature bounded from below
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• The Globalization Theorem for the Curvature Dimension Condition
• Local Poincaré inequalities from stable curvature conditions on metric spaces
• Riemannian Geometry