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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Author: Aino, Masayuki
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211171
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Convergence to the Product of the Standard Spheres and Eigenvalues of the Laplacian. Masayuki Aino. SIGMA 17 (2021), 017, 29 pages

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