ICTS:32657

Graph discretization of Riemannian manifolds with Ricci bounds: Approximating spectrum of the Laplacian

(2025). Graph discretization of Riemannian manifolds with Ricci bounds: Approximating spectrum of the Laplacian. SciVideos. https://scivideos.org/index.php/icts-tifr/32657

Graph discretization of Riemannian manifolds with Ricci bounds: Approximating spectrum of the Laplacian. SciVideos, Aug. 20, 2025, https://scivideos.org/index.php/icts-tifr/32657 

          @misc{ scivideos_ICTS:32657,
            doi = {},
            url = {https://scivideos.org/index.php/icts-tifr/32657},
            author = {},
            keywords = {},
            language = {en},
            title = {Graph discretization of Riemannian manifolds with Ricci bounds: Approximating spectrum of the Laplacian},
            publisher = {},
            year = {2025},
            month = {aug},
            note = {ICTS:32657 see, \url{https://scivideos.org/index.php/icts-tifr/32657}}
          }
Anusha Bhattacharya
Talk numberICTS:32657
Source RepositoryICTS-TIFR

Abstract

We study the approximation of eigenvalues for the Laplace-Beltrami operator on closed Riemannian manifolds in the class characterized by bounded Ricci curvature, a lower bound on the injectivity radius, and an upper bound on the diameter. We use an (\epsilon,\rho)-approximation of the manifold by a weighted graph, as introduced by Burago et al. By adapting their methods, we prove that as the parameters \epsilon, \rho and the ratio \frac{\epsilon}{\rho} approach zero, the k-th eigenvalue of the graph Laplacian converges uniformly to the k-th eigenvalue of the manifold's Laplacian for each k.