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In the manifold setting, we provide a series of spectral convergence results quantifying how the eigenvectors and eigenvalues of the graph Laplacian converge to the eigenfunctions and eigenvalues of the Laplace-Beltrami operator in the $L^\infty$ sense.
C1 isometric imbeddings
John Nash · 1954
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The numerical solution of the eigenvalue problem for compact integral operators
Kendall E Atkinson · 1967
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On the behavior of the fundamental solution of the heat equation with variable coefficients
Sathamangalam R Srinivasa Varadhan · 1967
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The spectral function of an elliptic operator
Lars Hörmander · 1968
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Foundations of global non-linear analysis
Richard S Palais · 1968
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Pointwise bounds on the space and time derivatives of heat kernels
E Brian Davies · 1989
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Embedding Riemannian manifolds by their heat kernel
Pierre Bérard, Gérard Besson, and Sylvain Gallot · 1994
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Spectral Graph Theory
Fan Chung · 1996
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Gaussian upper bounds for the heat kernel on arbitrary manifolds
Alexander Grigor’yan · 1997
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The Laplacian on a Riemannian manifold: an introduction to analysis on manifolds
Steven Rosenberg · 1997
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Ronald R Coifman and Stéphane Lafon · 2006
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Eigenfunctions of the Laplacian on compact Riemannian manifolds
Harold Donnelly · 2006
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Uniform convergence of adaptive graph-based regularization
Matthias Hein · 2006
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Amit Singer and Hau-Tieng Wu · 2016
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Extrinsic Gaussian processes for regression and classification on manifolds
Lizhen Lin, Niu Mu, Pokman Cheung, David Dunson, et al · 2018
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Nicolas Garcia Trillos, Moritz Gerlach, Matthias Hein, and Dejan Slepcev · 2018
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Think globally, fit locally under the manifold setup: Asymptotic analysis of locally linear embedding
Hau-Tieng Wu and Nan Wu · 2018
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Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-nn graphs
Jeff Calder and Nicolas Garcia Trillos · 2019
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Michael Reed · 2012
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Dmitri Burago, Sergei Ivanov, and Yaroslav Kurylev · 2015
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